Statistical Reversion Engine [JOAT]Statistical Reversion Engine
Introduction
The Statistical Reversion Engine (SRE) is an advanced open-source mean reversion indicator that combines statistical deviation bands, premium/discount zone analysis, DCA level calculation, Z-score measurement, and enhanced reversion probability scoring to identify high-probability mean reversion opportunities. This indicator quantifies price deviation from statistical mean using multiple calculation methods (SMA, EMA, VWAP, HMA) and provides probabilistic assessment of reversion likelihood through multi-factor analysis including deviation magnitude, volatility regime, and historical reversion patterns.
Unlike basic Bollinger Band indicators that simply plot standard deviation bands, SRE employs a sophisticated statistical framework that calculates Z-scores, premium/discount percentages, enhanced reversion probability (incorporating volatility and premium factors), and tracks historical reversion speed to provide traders with quantitative mean reversion intelligence. The indicator also generates DCA (Dollar Cost Averaging) levels with volatility-adjusted spacing for systematic position building.
Why This Indicator Exists
This indicator addresses the challenge of identifying when price has deviated sufficiently from mean to warrant mean reversion trades. Traditional mean reversion indicators lack probabilistic quantification and don't account for volatility regime or historical reversion patterns. SRE systematically reveals:
Multiple Mean Calculations: SMA, EMA, VWAP (session/continuous), HMA for flexible mean definition
Statistical Deviation Bands: 1σ, 2σ, 3σ bands with customizable multipliers
Z-Score Calculation: Quantifies deviation in standard deviation units
Premium/Discount Analysis: Percentage deviation from mean with zone classification
Enhanced Reversion Probability: Multi-factor scoring (Z-score + premium + volatility)
DCA Level Generation: Volatility-adjusted levels for systematic position building
Historical Reversion Tracking: Measures average bars to return to mean after extreme deviation
Each component provides unique intelligence. Mean calculation defines center, deviation bands show extremes, Z-score quantifies magnitude, premium/discount shows percentage, probability scores likelihood, DCA levels provide entry framework, and historical tracking provides context.
Core Components Explained
1. Flexible Mean Calculation System
SRE supports four mean calculation methods:
f_calculate_mean(string type, int length) =>
float result = close
if type == "SMA"
result := ta.sma(close, length)
else if type == "EMA"
result := ta.ema(close, length)
else if type == "VWAP"
result := session_reset ? ta.vwap(hlc3) : ta.vwma(hlc3, length)
else if type == "HMA"
result := ta.hma(close, length)
result
Mean selection impacts reversion behavior:
- SMA: Simple average, slower to respond
- EMA: Exponential weighting, faster response
- VWAP: Volume-weighted, institutional reference
- HMA: Hull Moving Average, smoothest with minimal lag
2. Statistical Deviation Band System
Three deviation bands calculated using standard deviation:
float mean_line = f_calculate_mean(mean_type, mean_length)
float stdev = f_calculate_stdev(close, deviation_period)
float upper_band_1 = mean_line + (stdev * band_multiplier_1) // 1σ
float lower_band_1 = mean_line - (stdev * band_multiplier_1)
float upper_band_2 = mean_line + (stdev * band_multiplier_2) // 2σ
float lower_band_2 = mean_line - (stdev * band_multiplier_2)
float upper_band_3 = mean_line + (stdev * band_multiplier_3) // 3σ
float lower_band_3 = mean_line - (stdev * band_multiplier_3)
Default multipliers: 1.0, 2.0, 3.0 (customizable)
- 1σ: 68% of price action (normal range)
- 2σ: 95% of price action (extended range)
- 3σ: 99.7% of price action (extreme range)
3. Z-Score Calculation & Classification
Z-score quantifies deviation in standard deviation units:
f_calculate_zscore(float price, float mean, float stdev) =>
float zscore = stdev > 0 ? (price - mean) / stdev : 0.0
zscore
float zscore = f_calculate_zscore(close, mean_line, stdev)
Z-score interpretation:
- |Z| < 1.0: Normal deviation (40% reversion probability)
- |Z| 1.0-1.5: Moderate deviation (60% reversion probability)
- |Z| 1.5-2.0: Extended deviation (75% reversion probability)
- |Z| 2.0-2.5: Extreme deviation (85% reversion probability)
- |Z| > 3.0: 3-sigma event (95% reversion probability)
4. Premium/Discount Zone Analysis
Percentage deviation from mean with zone classification:
f_calculate_premium_discount(float price, float mean) =>
float pct = mean > 0 ? ((price - mean) / mean) * 100 : 0.0
pct
float premium_discount_pct = f_calculate_premium_discount(close, mean_line)
string current_zone =
premium_discount_pct >= premium_threshold * 2 ? "Extreme Premium" :
premium_discount_pct >= premium_threshold ? "Premium" :
premium_discount_pct <= discount_threshold * 2 ? "Extreme Discount" :
premium_discount_pct <= discount_threshold ? "Discount" :
"Fair Value"
Zone classification (default thresholds):
- Extreme Premium: >3.0% above mean (strong sell zone)
- Premium: 1.5-3.0% above mean (sell zone)
- Fair Value: -1.5% to +1.5% (neutral zone)
- Discount: -3.0% to -1.5% below mean (buy zone)
- Extreme Discount: <-3.0% below mean (strong buy zone)
5. Enhanced Reversion Probability Scoring
Multi-factor probability calculation:
f_enhanced_reversion_prob(float z, float premium_pct, float vol_rank) =>
float base_prob = f_reversion_probability(z)
// Adjust for premium/discount magnitude
float premium_factor = math.abs(premium_pct) > 3 ? 1.2 :
math.abs(premium_pct) > 2 ? 1.1 :
math.abs(premium_pct) > 1 ? 1.0 : 0.9
// Adjust for volatility (lower vol = higher reversion probability)
float vol_factor = vol_rank < 30 ? 1.2 :
vol_rank < 50 ? 1.1 :
vol_rank < 70 ? 1.0 : 0.85
math.min(base_prob * premium_factor * vol_factor, 99)
Enhanced probability accounts for:
- Base Z-score probability
- Premium/discount magnitude (larger deviation = higher probability)
- Volatility regime (lower volatility = more predictable reversion)
6. Volatility-Adjusted DCA Level Generation
DCA levels automatically adjust spacing based on volatility:
float current_atr = ta.atr(14)
float atr_pct = close > 0 ? (current_atr / close) * 100 : 0
float vol_multiplier = atr_pct > 3 ? 1.5 : atr_pct > 2 ? 1.2 : atr_pct > 1 ? 1.0 : 0.8
for i = 1 to dca_levels
float adjusted_spacing = (dca_spacing * vol_multiplier) / 100
float buy_level = mean_line * (1 - adjusted_spacing * i)
float sell_level = mean_line * (1 + adjusted_spacing * i)
array.push(dca_buy_levels, buy_level)
array.push(dca_sell_levels, sell_level)
Volatility adjustment:
- High vol (ATR% >3): 1.5x spacing (wider levels)
- Elevated vol (ATR% 2-3): 1.2x spacing
- Normal vol (ATR% 1-2): 1.0x spacing (default)
- Low vol (ATR% <1): 0.8x spacing (tighter levels)
7. Historical Reversion Speed Tracking
Measures average bars to return to mean after extreme deviation:
var array reversion_times = array.new_int(0)
var bool tracking_reversion = false
var int reversion_start_bar = 0
if math.abs(zscore) >= 2.5 and not tracking_reversion
tracking_reversion := true
reversion_start_bar := bar_index
if tracking_reversion and math.abs(zscore) < 0.5
int reversion_time = bar_index - reversion_start_bar
array.push(reversion_times, reversion_time)
tracking_reversion := false
float avg_reversion_time = array.size(reversion_times) > 0 ?
array.avg(reversion_times) : na
Average reversion time provides context for expected holding period.
Visual Elements
Mean Line: Electric lime line showing statistical mean
Deviation Bands: 1σ (lime), 2σ (violet), 3σ (deep violet) with gradient fills
Premium/Discount Zones: Background coloring (violet for premium, lime for discount)
DCA Levels: Dotted lines with "B1, B2, B3..." (buy) and "S1, S2, S3..." (sell) labels
Z-Score Label: Current Z-score displayed on price
Gradient Zone Fills: Progressive transparency between bands
Mean Reversion Signals: Triangle markers for strong buy/sell setups
Reversion Probability Heatmap: Background intensity based on enhanced probability
Dashboard: Real-time metrics including zone, P/D%, Z-score, reversion probability, mean value, distance, enhanced probability, deviation percentile, mean trend, nearest DCA, average reversion time, bars since extreme
Input Parameters
Mean Calculation:
Mean Type: SMA, EMA, VWAP, HMA (default: VWAP)
Mean Length: Period for mean calculation (default: 20)
Session Reset (VWAP): Toggle session anchoring (default: true)
Deviation Bands:
Band 1 Multiplier: 1σ multiplier (default: 1.0)
Band 2 Multiplier: 2σ multiplier (default: 2.0)
Band 3 Multiplier: 3σ multiplier (default: 3.0)
Deviation Period: Standard deviation calculation period (default: 20)
Premium/Discount:
Premium Threshold (%): Threshold for premium zone (default: 1.5%)
Discount Threshold (%): Threshold for discount zone (default: -1.5%)
DCA Levels:
Enable DCA Levels: Toggle DCA display (default: true)
Number of DCA Levels: Levels to generate (default: 5)
DCA Spacing (%): Base spacing between levels (default: 1.5%)
Visualization:
Show Deviation Bands: Toggle band display (default: true)
Show Band Fills: Toggle gradient fills (default: true)
Show Premium/Discount Zones: Toggle background coloring (default: true)
Show Z-Score Label: Toggle Z-score display (default: true)
How to Use This Indicator
Step 1: Identify Current Zone
Check dashboard "Zone" row. Extreme Discount = strong buy zone, Extreme Premium = strong sell zone.
Step 2: Assess Z-Score Magnitude
|Z| >2.0 indicates extended deviation. |Z| >3.0 is 3-sigma event (rare, high reversion probability).
Step 3: Check Enhanced Reversion Probability
Dashboard shows enhanced probability accounting for volatility and premium factors. >80% is high probability.
Step 4: Monitor Mean Trend
"Rising" mean suggests uptrend, "Falling" suggests downtrend. Trade with mean trend for higher probability.
Step 5: Use DCA Levels for Entry
Enter positions at DCA levels (B1, B2, B3 for longs; S1, S2, S3 for shorts) to average into position.
Step 6: Wait for Strong Signals
Triangle markers appear when:
- Extreme zone + enhanced probability >80% + band crossover
- These are highest conviction mean reversion setups
Best Practices
Mean reversion works best in ranging markets - avoid strong trends
3-sigma events (|Z| >3.0) have highest reversion probability but occur rarely
Use DCA levels to build positions systematically rather than all-in entries
Enhanced probability >80% indicates high-quality setup
Mean trend provides context - reversion against trend is lower probability
Volatility-adjusted DCA spacing prevents over-concentration in high vol
Average reversion time helps set realistic profit target timeframes
Combine with higher timeframe trend - mean reversion with trend is safer
Deviation percentile >90% indicates extreme deviation
Bars since extreme >50 suggests extended deviation may persist
Indicator Limitations
Mean reversion fails during strong trending markets
3-sigma events can persist longer than expected during major news
DCA levels don't account for fundamental catalysts
Enhanced probability is statistical, not deterministic
Historical reversion time doesn't guarantee future reversion speed
VWAP mean resets daily - may not be appropriate for all timeframes
Standard deviation assumes normal distribution - markets have fat tails
Premium/discount thresholds may need adjustment for different instruments
Technical Implementation
Built with Pine Script v6 using:
Four mean calculation methods (SMA, EMA, VWAP, HMA)
Three-tier deviation band system with customizable multipliers
Z-score calculation with standard deviation
Premium/discount percentage with zone classification
Enhanced reversion probability (Z-score + premium + volatility)
Volatility-adjusted DCA level generation
Historical reversion speed tracking with arrays
Deviation percentile ranking
Mean trend detection (fast vs slow mean)
Gradient zone fills with progressive transparency
Reversion probability heatmap background
Comprehensive dashboard with 12 metrics
The code is fully open-source and can be modified to suit individual trading styles.
Originality Statement
This indicator is original in its comprehensive statistical mean reversion approach. While Bollinger Bands and mean reversion are established concepts, this indicator is justified because:
It combines four mean calculation methods with three-tier deviation bands
Enhanced reversion probability incorporates Z-score, premium magnitude, and volatility regime
Volatility-adjusted DCA level generation adapts to market conditions
Historical reversion speed tracking provides empirical context
Premium/discount zone classification adds percentage-based perspective
Mean trend detection (fast vs slow) provides directional context
Deviation percentile ranking shows historical extremity
Integration of statistical measures (Z-score, stdev, percentile) with practical tools (DCA levels, signals)
Each component contributes unique information: mean defines center, deviation bands show extremes, Z-score quantifies magnitude, premium/discount shows percentage, enhanced probability scores likelihood, DCA levels provide framework, historical tracking provides context, and mean trend shows direction. The indicator's value lies in presenting these complementary perspectives simultaneously with unified statistical framework.
Disclaimer
This indicator is provided for educational and informational purposes only. It is not financial advice. Mean reversion probabilities do not guarantee outcomes. Trading involves substantial risk of loss. Past performance does not guarantee future results. Always use proper risk management and never risk more than you can afford to lose.
-Made with passion by officialjackofalltrades Indicator
Probabilistic Bias Engine [JOAT]Probabilistic Bias Engine
Introduction
The Probabilistic Bias Engine (PBE) is an advanced open-source directional bias indicator that combines Bayesian probability analysis, historical for-loop pattern recognition, multi-timeframe confluence detection, and ensemble learning to quantify market directional bias with statistical confidence. This indicator transforms raw price action into probabilistic bias scores (0-100%), helping traders identify high-probability directional setups through systematic analysis of historical price behavior across multiple timeframes.
Unlike simple trend indicators that use moving averages or momentum oscillators, PBE employs a sophisticated for-loop analysis system that compares current price against historical price points across customizable lookback periods, applies Bayesian probability theory to calculate directional likelihood, and aggregates signals across multiple timeframes to generate confidence-weighted bias scores. The indicator provides both current timeframe bias and multi-timeframe confluence analysis for comprehensive directional assessment.
Why This Indicator Exists
This indicator addresses the challenge of quantifying directional bias with statistical rigor. Traditional trend indicators provide binary signals (bullish/bearish) without probability quantification. PBE systematically analyzes historical price behavior to reveal:
Bayesian Probability Calculation: Converts for-loop analysis into probabilistic bias scores using Bayesian inference
Historical Pattern Recognition: Analyzes price position relative to 1-70 historical bars to identify directional patterns
Multi-Timeframe Confluence: Confirms bias across short (5m), medium (15m), and long (60m) timeframes
Ensemble For-Loop Analysis: Combines multiple lookback periods (30, 70, 150 bars) for robust bias calculation
Volatility Regime Scaling: Adjusts probability scores based on current volatility environment
Divergence Confirmation Layer: Detects RSI divergences to enhance signal quality
Confidence Heatmap: Visualizes setup quality through multi-factor confidence scoring (0-100%)
Each component provides unique intelligence. For-loop analysis shows historical price position, Bayesian calculation quantifies probability, MTF confluence shows conviction, ensemble analysis adds robustness, volatility scaling adjusts for regime, divergence layer confirms reversals, and confidence scoring synthesizes all factors.
Core Components Explained
1. For-Loop Historical Analysis
PBE's core innovation is systematic comparison of current price against historical price points:
f_forloop_analysis(float src, int start, int lookback) =>
float sum = 0.0
for i = start to lookback
sum += src > src ? 1 : -1
float normalized = sum / (lookback - start + 1)
normalized
This function iterates through historical bars, adding +1 when current price is above historical price and -1 when below. The normalized result ranges from -1.0 (price below all historical points) to +1.0 (price above all historical points).
2. Bayesian Probability Calculation
The for-loop score is converted to probability using Bayesian inference:
f_bayesian_probability(float loop_value) =>
float evidence = loop_value > 0 ? 0.7 : 0.3
float prior = 0.5
float posterior = (prior * evidence) /
(prior * evidence + (1 - prior) * (1 - evidence))
posterior
This calculates the posterior probability of bullish bias given the for-loop evidence. Positive loop values increase bullish probability, negative values increase bearish probability. The result is scaled to 0-100% for display.
image]https://www.pulsewire.com/x/CtYqgABU/
3. Multi-Timeframe Confluence Detection
PBE requests bias data from three timeframes and counts alignment:
f_get_timeframe_bias(string tf) =>
= request.security(syminfo.tickerid, tf,
)
float prob_tf = f_bayesian_probability(loop_score_tf)
int bias_tf = prob_tf > 0.5 ? 1 : -1
Confluence is calculated by counting how many timeframes agree:
Strong Aligned (4/4): All timeframes bullish or bearish - highest conviction
Aligned (3/4): Majority alignment - moderate conviction
Weak (2/4): Split alignment - low conviction
No Alignment (1/4 or 0/4): Conflicting signals - no conviction
4. Ensemble For-Loop Analysis
Multiple lookback periods are combined for robust bias calculation:
f_forloop_ensemble(float src, int start, int end1, int end2, int end3) =>
// Calculate for-loop scores for 30, 70, and 150 bar lookbacks
float norm1 = sum1 / (end1 - start + 1)
float norm2 = sum2 / (end2 - start + 1)
float norm3 = sum3 / (end3 - start + 1)
// Weighted ensemble (shorter periods get more weight)
float ensemble = (norm1 * 0.5) + (norm2 * 0.3) + (norm3 * 0.2)
ensemble
Short-term bias (30 bars) receives 50% weight, medium-term (70 bars) receives 30%, and long-term (150 bars) receives 20%. This creates a balanced view across multiple time horizons.
5. Volatility Regime Scaling
Probability scores are adjusted based on volatility environment:
float atr_val = ta.atr(14)
float natr = (atr_val / close) * 100
float vol_percentile = ta.percentrank(natr, 100)
float regime_multiplier =
vol_percentile >= 80 ? 0.85 : // High vol: reduce confidence
vol_percentile >= 60 ? 0.92 : // Elevated: slight reduction
vol_percentile >= 40 ? 1.0 : // Normal: no adjustment
vol_percentile >= 20 ? 1.05 : // Low vol: slight increase
1.1 // Very low: increase confidence
float regime_adjusted_prob = smoothed_probability * regime_multiplier
High volatility reduces probability scores (more uncertainty), while low volatility increases scores (more predictable).
6. Divergence Confirmation Layer
RSI divergences are detected to enhance signal quality:
float rsi = ta.rsi(close, 14)
// Bullish divergence: price lower low, RSI higher low
bool bull_divergence = low < last_rsi_low_price and rsi > last_rsi_low
// Bearish divergence: price higher high, RSI lower high
bool bear_divergence = high > last_rsi_high_price and rsi < last_rsi_high
Divergences add 20 points to confidence score and trigger enhanced signals when combined with probability alignment.
7. Confidence Heatmap Visualization
Multi-factor confidence scoring (0-100%) based on:
Probability Strength (0-40 points): Distance from 50% neutral (max 40 points at 100% or 0%)
MTF Alignment (0-30 points): 30 points for 4/4 alignment, 20 for 3/4, 10 for 2/4
Divergence Confirmation (0-20 points): 20 points when divergence detected
Regime Favorability (0-10 points): 10 points for Normal/Low vol, 5 for Very Low, 0 for High vol
Total confidence score determines background heatmap intensity:
80-100%: Strong signal (bright color, low transparency)
60-79%: Moderate signal (medium color, medium transparency)
40-59%: Weak signal (dim color, high transparency)
0-39%: No signal (neutral color)
Visual Elements
Probability Line: Main plot showing smoothed probability (0-100%) with dynamic coloring
Zero-Lag Line: Circles overlay showing zero-lag probability for early signals
Histogram: Gradient-colored histogram showing probability deviation from 50% neutral
Reference Lines: 70% (strong bullish), 50% (neutral), 30% (strong bearish)
Background Zones: Strong bullish (>70%), strong bearish (<30%) with transparency
Confidence Heatmap: Background intensity based on multi-factor confidence score
Signal Shapes: High conviction bull/bear setups, regime shifts, divergence confirmations
Dashboard: Real-time metrics including current probability, strength, MTF alignment, ensemble score, volatility regime, confidence, and divergence status
Input Parameters
Bayesian Parameters:
Price Source: Data source for calculations (default: hlc3)
Bayesian Period: Smoothing period for probability (default: 14)
Signal Smoothing: EMA smoothing for final probability (default: 2)
Historical Analysis:
Loop Start: Starting bar for for-loop analysis (default: 1)
Loop Lookback: Ending bar for for-loop analysis (default: 70)
Multi-Timeframe Confluence:
Enable MTF Confluence: Toggle multi-timeframe analysis (default: enabled)
Short Timeframe: Fast timeframe for confluence (default: 5m)
Medium Timeframe: Medium timeframe for confluence (default: 15m)
Long Timeframe: Slow timeframe for confluence (default: 60m)
Confluence Requirement: Minimum timeframes required (default: 2)
Visualization:
Show Probability Bands: Toggle 70%/30% reference lines
Show Bias Zones: Toggle background coloring for strong bias
Show Histogram: Toggle probability deviation histogram
How to Use This Indicator
Step 1: Monitor Probability Level
Watch the main probability line. >70% indicates strong bullish bias, <30% indicates strong bearish bias, 40-60% is neutral.
Step 2: Check MTF Confluence
Verify dashboard shows "Strong Aligned" or "Aligned" status. Higher alignment = higher conviction.
Step 3: Assess Confidence Score
Dashboard confidence >70% indicates high-quality setup. >80% is exceptional.
Step 4: Confirm with Ensemble
Ensemble probability should align with current probability. Divergence suggests conflicting time horizons.
Step 5: Consider Volatility Regime
"Normal" or "Low Vol" regimes have higher reliability. "High Vol" regimes require extra caution.
Step 6: Wait for High Conviction Signals
Best setups occur when:
- Probability >65% or <35%
- Confidence >70%
- MTF alignment 3/4 or 4/4
- Cooldown period passed (12+ bars since last signal)
Best Practices
Use probability crossovers of 50% as regime shift signals
Combine with price action - probability shows bias, price shows execution
MTF alignment is most reliable during trending markets
Confidence heatmap provides quick visual assessment of setup quality
Divergence signals add significant edge when combined with probability alignment
Ensemble probability provides longer-term context - use for position bias
Volatility regime scaling is critical - reduce size in high vol environments
Zero-lag line provides early warning of probability shifts
Histogram intensity shows conviction - larger bars = stronger bias
Indicator Limitations
For-loop analysis is computationally intensive - may slow on lower-end devices
Probability scores are based on historical patterns - unprecedented events can invalidate
MTF confluence requires sufficient data on all timeframes
Bayesian calculation assumes price behavior follows historical patterns
High volatility reduces probability reliability - regime scaling helps but doesn't eliminate
Divergence detection requires clear pivot formation - may lag in choppy markets
Confidence scoring is multi-factor but still probabilistic - not deterministic
Zero-lag calculation can produce whipsaws during consolidation
Technical Implementation
Built with Pine Script v6 using:
Custom for-loop historical analysis across 1-70 bars
Bayesian probability calculation with evidence-based inference
Multi-timeframe security requests for 5m, 15m, 60m confluence
Ensemble for-loop analysis with weighted averaging (30, 70, 150 bars)
ATR-based volatility regime classification with percentile ranking
RSI divergence detection using pivot analysis
Multi-factor confidence scoring (probability, MTF, divergence, regime)
Zero-lag EMA calculation for early signal detection
Gradient histogram with dynamic coloring based on probability
Confidence heatmap background with intensity scaling
Signal cooldown system (12 bars minimum) to prevent overtrading
The code is fully open-source and can be modified to suit individual trading styles.
Originality Statement
This indicator is original in its probabilistic bias quantification approach. While for-loop analysis and Bayesian probability are established concepts, this indicator is justified because:
It combines systematic for-loop historical analysis with Bayesian probability theory for statistical rigor
The ensemble for-loop system (30, 70, 150 bars) with weighted averaging is unique
Multi-timeframe confluence detection provides conviction measurement across 4 timeframes
Volatility regime scaling adjusts probability scores based on market environment
Divergence confirmation layer adds reversal detection to directional bias
Multi-factor confidence scoring (probability + MTF + divergence + regime) synthesizes all components
Zero-lag overlay provides early warning system for probability shifts
Confidence heatmap visualization makes setup quality immediately apparent
Each component contributes unique information: for-loop shows historical position, Bayesian quantifies probability, MTF shows conviction, ensemble adds robustness, volatility scales for regime, divergence confirms reversals, confidence synthesizes quality, and zero-lag provides early warning. The indicator's value lies in presenting these complementary perspectives simultaneously with unified probabilistic framework.
Disclaimer
This indicator is provided for educational and informational purposes only. It is not financial advice. Probability scores do not guarantee outcomes. Trading involves substantial risk of loss. Past performance does not guarantee future results. Always use proper risk management and never risk more than you can afford to lose.
-Made with passion by officialjackofalltrades Indicator
Directional Logistic Oscillator | GainzAlgoOverview
The Directional Logistic Oscillator (DLO) is a momentum-based indicator designed to measure directional market strength and identify potential trend reversals or mean-reversion opportunities. It builds on the classic Directional Movement Index (DMI) by transforming its components (+DI, -DI, and ADX) into probabilistic signals using logistic functions, then combining them into a bounded oscillator that oscillates between approximately -1 and +1.
Unlike traditional oscillators like RSI or MACD, DLO emphasizes directional probability by estimating the likelihood of bullish or bearish dominance while factoring in overall trend strength (via ADX). This makes it particularly useful for:
Spotting overbought/oversold conditions in ranging markets.
Confirming trend shifts in trending markets.
Generating reversal signals based on oscillator cycles.
The oscillator is plotted as histogram bars (columns) for visual clarity, with color-coding to highlight strength and direction. Positive values indicate bullish momentum, negative values bearish, and crossings of key levels can signal trading opportunities.
How It Works
At its core, DLO processes DMI data through a logistic transformation to create "probabilities" of directional movement:
1. DMI Calculation : Uses the standard DMI with a user-defined length (default 14) to compute +DI (upward movement), -DI (downward movement), and ADX (trend strength).
2. Logistic Probability : Each DMI component is normalized against its long-term mean and passed through a logistic (sigmoid) function. This creates smooth probabilities between 0 and 1.
The logistic function is defined as:
logistic_prob(series, mean_lb, slope, smooth_len) =>
mean = ta.sma(series, mean_lb)
z = (series - mean) * slope
prob_raw = 1.0 / (1.0 + math.exp(-z))
ta.ema(prob_raw, smooth_len)
This step makes the indicator adaptive to market conditions, with the "slope" controlling how sharply it reacts to deviations from the mean.
3. Net Directional Strength : Bullish minus bearish probability, scaled by ADX probability and a user-defined multiplier, then bounded using a hyperbolic tangent (tanh) function to keep values between -1 and +1.
net_dir = prob_plus - prob_minus
strength_raw = net_dir * prob_adx * osc_scale
strength_bound = tanh(strength_raw)
Tanh ensures smooth, bounded output without clipping extremes unnaturally.
4. Smoothing and Signals: The raw strength is smoothed with EMA, then further processed into SMA and EMA lines for signal generation. Percentile-based thresholds (adaptive over a lookback period) detect extreme zones for mean-reversion signals.
The result is a visually intuitive oscillator: Green bars for bullish, red for bearish, with varying intensity based on momentum.
Inputs
DLO offers customizable settings grouped for ease of use. Defaults are tuned for balanced performance on daily charts.
DMI Settings
DI Length (default: 14): Controls DMI sensitivity. Shorter lengths react faster to price changes but add noise; longer lengths smooth signals for trends.
Mean Lookback (default: 360): The period for calculating the long-term average of DMI components. Higher values provide a more stable baseline, reducing false signals from short-term volatility. Lower values make the indicator more responsive but noisier
Difference between high and low mean lookback period, lower length can pick up on new trends faster but at the cost of increased noise.
Logistic Probability Settings
LR Slope (higher = steeper) (default: 0.18): Adjusts the steepness of the logistic curve. Lower values create gradual transitions (smoother oscillator); higher values make sharp shifts, emphasizing extremes.
Probability Smoothing (EMA) (default: 3): Short EMA to reduce noise in probabilities. Keep low (1-5) for responsiveness; higher for smoothness.
Oscillator Settings
Oscillator Scale (pre-tanh) (default: 2.5): Multiplies net strength before bounding. Higher values increase sensitivity and amplitude (larger swings); lower values compress the range for subtler signals.
Comparison of 4 different settings for Oscillator scale, showing that as the scale parameter increases, the oscillator output becomes more pronounced, exhibiting higher amplitude compression toward the bounds and spending more time saturated near the extreme values of +1 and −1.
Oscillator Smoothing Length (default: 7): Period for SMA/EMA smoothing of the final oscillator. Longer = smoother, fewer signals; shorter = more reactive.
Color & Display Settings
Buy Color / Sell Color: Customize colors for bullish/bearish visuals.
Plot Reversion Signals (default: true): Shows arrows for cycle reversals (local highs/lows).
Plot Mean-Reversion Signals (default: true): Arrows for crossings from extreme percentile zones.
Plot Oscillator MA (default: false): Overlays an SMA on the oscillator for additional confirmation.
Allow Intrabar Updating (default: true): Enables real-time updates within incomplete bars (may cause minor repainting).
Visuals
Oscillator Histogram: Columns colored green (bullish) or red (bearish), with lighter shades for weaker momentum. Crosses above/below zero signal momentum shifts.
Horizontal Lines: Zero (neutral), +0.5 (strong bullish), -0.5 (strong bearish).
Background Highlights: Subtle green/red shading when in strong zones.
Bar Colors: Mirrors oscillator direction on the price chart.
Color-coded trend regimes: green/teal highlight strong and weak uptrends, red/purple mark strong and weak downtrends, while the oscillator histogram confirms direction and strength through its polarity and amplitude.
Signals
Mean-Reversion (MR) Signals : Triangles (▲/▼) when the smoothed oscillator crosses up from low percentiles (oversold) or down from high percentiles (overbought). These are adaptive, using historical data for dynamic extremes.
Buy: Oscillator crosses above lower threshold (e.g., 10th/5th percentile).
Sell: Crosses below upper threshold (e.g., 90th/95th percentile).
Reversion Signals : Arrows (⬆/⬇) at local turning points in the oscillator cycle, indicating potential reversals.
Zero-Line Crosses : Basic bullish/bearish momentum changes.
Usage Tips
Trend Confirmation: Use in trending markets—persistent positive/negative values confirm up/down trends. Pair with moving averages for entries.
Mean-Reversion: In sideways markets, trade MR signals from extremes. Combine with support/resistance.
Divergences: Look for price making new highs/lows while DLO doesn't for reversal setup.
Alerts
MR Buy/Sell: Extreme zone crosses (percentile-based).
Reversion Up/Down: Cycle turning points.
Osc Bullish/Bearish Cross: Zero-line crosses.
Limitations
Like all oscillators, DLO can lag in strong trends or produce false signals in choppy markets, use with confirmation.
Percentile thresholds adapt over time but may vary by asset volatility.
Not a standalone system; always combine with risk management.
Indicator
Indicator
Indicator
Market Regime AnalyzerStatistical regime detection with forward-looking transition probabilities. Combines drift testing, variance ratios, and volume delta to classify markets into 5 regimes and quantify transition probabilities.
What Regime Are We In, and What's Likely Next?
That's the question this indicator answers with statistical rigor and forward-looking probabilities.
The Problem:
Most traders classify regimes arbitrarily: "Bull if price > 200 MA" or "Bear if RSI < 30." These rules ignore statistical significance, volume confirmation, and mean reversion patterns. The result? Late entries, false signals, and confusion when markets transition.
The Solution:
Market Regime Analyzer combines drift detection, variance ratio testing, and volume delta analysis to classify markets into 5 distinct regimes. Then it calculates the probability of transitioning to each regime based on historical patterns.
The Benefit:
Know not just where you are, but where you're likely going - with probabilities, not guesses.
The Five Market Regimes
🟢 Strong Bull (Regime 1)
- Statistically significant upward drift (t-stat > 1.96)
- Strong buying pressure (volume delta > 0.3)
- No mean reversion detected
- **Trade:** Trend-following strategies, ride the momentum
🟢 Weak Bull (Regime 2)
- Upward drift present
- BUT weak volume OR mean reversion detected
- **Trade:** Reduce position size, tighten stops, prepare for consolidation
⚪ Consolidation (Regime 3)
- No statistically significant drift
- Mixed volume signals
- Mean reversion likely present
- **Trade:** Range-trading, avoid trend-following systems
🔴 Weak Bear (Regime 4)
- Downward drift present
- BUT weak volume pressure
- **Trade:** Cautious shorts, reduce exposure, prepare for bounce
🔴 Strong Bear (Regime 5)
- Statistically significant downward drift (t-stat < -1.96)
- Strong selling pressure (volume delta < -0.3)
- No mean reversion detected
- **Trade:** Trend-following shorts, protective puts
The Statistical Framework
1. Drift Detection with T-Statistics
Instead of guessing if there's a trend, we test it statistically.
How it works:
- Calculates mean return over lookback period
- Standardizes by volatility
- Compares to significance threshold (default 1.96 = 95% confidence)
What it tells you:
- T-stat > 1.96: Statistically significant uptrend
- T-stat < -1.96: Statistically significant downtrend
- In between: No significant trend (consolidation)
Why it matters:
Only trades trends that are statistically validated, not just visually apparent.
2. Mean Reversion Testing (Variance Ratio)
Based on Lo & MacKinlay (1988) research, this detects when markets are range-bound.
How it works:
- Compares variance at different time scales
- Variance Ratio < 0.8 indicates mean reversion
What it tells you:
- Mean reversion = NO: Trends can continue
- Mean reversion = YES: Expect price to return to mean, not breakout
Why it matters:
Prevents chasing breakouts in range-bound markets.
3. Volume Delta Analysis
Total volume tells you HOW MUCH traded. Volume delta tells you WHO won.
How it works:
- Buying pressure - Selling pressure = Volume Delta
- Normalized to show relative strength
What it tells you:
- Strong positive delta (>0.3): Buyers in control
- Strong negative delta (<-0.3): Sellers in control
- Weak delta: No clear winner
Why it matters:
Price can move up on weak buying or down on weak selling. Volume delta reveals the truth.
4. Transition Probability Matrix
Historical regime changes predict future regime changes.
How it works:
- Tracks every regime transition over last 100 bars (configurable)
- Builds probability distribution for next regime
- Updates continuously
Example:
Current: Strong Bull
Historical transitions from Strong Bull:
- Stayed Strong Bull: 45%
- Became Weak Bull: 30%
- Became Consolidation: 20%
- Became Weak Bear: 4%
- Became Strong Bear: 1%
What it tells you:
Strong Bull has 75% chance of staying bullish (45% + 30%), only 5% chance of bearish turn.
Why it matters:
Adapts to your specific market's behavior patterns.
How to Use This Indicator
Strategy Adaptation
In Strong Bull/Bear Regimes:
- Use trend-following strategies
- Wider stops, let winners run
- Add to positions on pullbacks
- High confidence in directional trades
In Weak Bull/Bear Regimes:
- Reduce position sizes by 50%
- Tighter stops
- Take profits earlier
- Prepare for regime change
In Consolidation:
- Switch to range-trading strategies
- Avoid trend-following systems
- Sell resistance, buy support
- Wait for regime change before trend trades
Risk Management
Position Sizing:
- Strong regime + high continuation probability (>60%) = Normal size
- Weak regime OR high transition probability = Half size
- Consolidation = Quarter size or skip
Stop Loss Placement:
- Strong regime: Use wider stops (2x ATR)
- Weak regime: Tighter stops (1x ATR)
- Consolidation: Very tight stops (0.5x ATR)
Entry Timing
Best entries:
- Regime just changed to Strong Bull/Bear
- High probability (>50%) of staying in current regime
- No divergence signals present
- Drift and volume delta aligned
Avoid entries:
- High probability of regime change
- Divergence signals appearing
- Mean reversion detected in trending regime
- Weak volume despite price movement
Reading the Dashboard
Current Regime
Color-coded for instant recognition:
- Dark Green = Strong Bull
- Light Green = Weak Bull
- Gray = Consolidation
- Light Red = Weak Bear
- Dark Red = Strong Bear
Annualized Drift
Expected annual return based on recent trend.
- Positive = Upward bias
- Negative = Downward bias
- Near zero = No directional edge
T-Statistic
Measures statistical significance of drift.
- > 1.96 = 95% confident in uptrend
- < -1.96 = 95% confident in downtrend
- Between = Not statistically significant
Mean Reversion
- Yes = Expect price to return to mean (range-bound)
- No = Trends can continue (trending market)
Volume Pressure
Normalized volume delta strength.
- > 0.3 = Strong buying
- < -0.3 = Strong selling
- Near 0 = Balanced
Transition Probabilities
Shows most likely next regime.
- Highest probability = Most likely outcome
- Evenly distributed = High uncertainty
- Concentrated = High confidence in direction
Practical Examples
Example 1: Strong Bull with High Continuation
Dashboard shows:
Current Regime: Strong Bull
Drift: +22% annualized
T-Stat: 3.2
Mean Reversion: No
Volume Pressure: +0.45
Probabilities:
→ Strong Bull: 50%
→ Weak Bull: 25%
→ Consolidation: 20%
→ Bears: 5%
Interpretation:
- Strong uptrend (t-stat 3.2 >> 1.96)
- No mean reversion = trends can continue
- Strong buying pressure (0.45 > 0.3)
- 75% chance stays bullish (50% + 25%)
Action:
- Full position size on long setups
- Use trend-following entries
- Wider stops (2x ATR)
- High conviction trades
Example 2: Weak Bull Before Consolidation
Dashboard shows:
Current Regime: Weak Bull
Drift: +8% annualized
T-Stat: 1.2
Mean Reversion: Yes
Volume Pressure: +0.15
Probabilities:
→ Strong Bull: 10%
→ Weak Bull: 30%
→ Consolidation: 50%
→ Weak Bear: 10%
Interpretation:
- Weak drift (t-stat 1.2 < 1.96)
- Mean reversion detected = range-bound likely
- Weak volume (0.15 < 0.3)
- 50% chance of consolidation
Action:
- Reduce long positions
- Tighten stops
- Prepare for range-bound trading
- Avoid new trend trades
Example 3: Regime Transition Alert
Previous: Weak Bull
Current: Consolidation
Volume divergence signal appeared:
Price made new high, volume delta weakened
Interpretation:
- Trend exhausted
- Buyers losing control
- Regime confirmed the transition
Action:
- Exit trend-following longs
- Switch to range-trading approach
- Wait for new regime before new directional trades
Settings Guide
### Regime Detection Period (50)
Number of bars for statistical calculations.
- **30-40:** More responsive, catches changes faster, more regime switches
- **50 (default):** Balanced for daily/4H charts
- **75-100:** More stable, fewer false regime changes, slower to adapt
Transition History Depth (100)
How much history to use for probabilities.
- **50-75:** Adapts quickly to recent behavior
- **100 (default):** Balanced robustness
- **150-200:** More stable probabilities, slower to adapt
Volume Delta Period (14)
Period for volume calculations.
- **7-10:** More sensitive to volume shifts
- **14 (default):** Standard period
- **20-30:** Smoother, less noise
Significance Threshold (1.96)
T-statistic required for trend classification.
- **1.64:** 90% confidence, more trend regimes detected
- **1.96 (default):** 95% confidence, balanced
- **2.58:** 99% confidence, very conservative, mostly consolidation
Best Practices
Do:
- Wait for regime confirmation (at least 3-5 bars in new regime)
- Use probabilities to size positions appropriately
- Combine with support/resistance for entries
- Respect mean reversion signals
- Adapt strategy to current regime
Don't:
- Trade every regime change immediately
- Ignore high transition probabilities
- Use trend strategies in consolidation
- Override statistical signals with gut feel
- Trade against Strong regimes without clear setup
Timeframe Recommendations
Daily Charts:
- Default settings work well
- Most reliable regime detection
- Best for swing trading
4H Charts:
- Use default or slightly higher lookback (60-75)
- Good for active swing trading
- More regime changes than daily
1H Charts:
- Reduce lookback to 30-40
- More noise, use with caution
- Better for intraday position trading
15M and below:
- Not recommended
- Too much noise for statistical validity
- Regimes change too frequently
Combining with Other Indicators
Works Well With:
Moving Averages
- Use regime for directional bias
- MAs for specific entry/exit points
Support/Resistance
- Regime shows context
- S/R shows specific levels
- High probability at confluence
Volume Profile
- Regime shows regime
- Profile shows where volume is
- Target high-volume nodes
RSI/MACD
- Regime provides context
- Momentum shows entry timing
- Combine for higher probability
Example Combined Setup
Regime: Strong Bull
Price: Above 200 MA
Level: Pullback to support
RSI: Oversold (30)
Volume Delta: Still positive
Setup: Long entry
Reason: Trend intact, healthy pullback, buyers still present
Divergence Signals
The indicator shows volume divergence warnings:
Bearish Divergence (Red Triangle Down)
- Price makes new high
- Volume delta makes lower high
- Warning: Buyers weakening, potential reversal
Bullish Divergence (Green Triangle Up)
- Price makes new low
- Volume delta makes higher low
- Warning: Sellers weakening, potential reversal
How to use:
- Divergence in Strong regime = early warning of regime change
- Confirms when regime actually transitions
- Don't trade divergence alone, wait for regime confirmation
Limitations
This Indicator Cannot:
**Predict black swan events** - Unexpected news overrides all technical regimes
**Work in all markets** - Needs liquid markets with reliable volume data
**Guarantee profits** - Probabilities are not certainties
**Replace fundamental analysis** - Technical regimes can diverge from fundamentals
Works Best:
- Liquid markets (major indices, forex, crypto, large-cap stocks)
- Daily and 4H timeframes
- Combined with other analysis
- With proper risk management
- In normal market conditions
Common Questions
"Why did the regime stay consolidation despite strong price move?"
The indicator detected mean reversion (variance ratio < 0.8), indicating the move will likely reverse. Or the move wasn't statistically significant (t-stat < 1.96). Trust the statistics over visual appearance.
"Probabilities show 30% for each regime. What does that mean?"
High uncertainty. The market is at an inflection point. Reduce position sizes and wait for clearer regime formation.
"Can I use this for day trading?"
Not recommended on timeframes below 1H. Statistical tests need sufficient data. Better suited for swing trading.
"Why does this show Strong Bull when my momentum indicators show weakness?"
Momentum can weaken while the trend remains statistically significant. The indicator focuses on drift and volume, not momentum. Consider it a different perspective.
Technical Notes
Volume Delta Approximation
Uses OHLCV data to approximate order flow:
- Buy volume ≈ Volume on up-closes
- Sell volume ≈ Volume on down-closes
- Delta = Buy - Sell
**Note:** Real order flow (from futures or Level 2) is more precise. This approximation works well on liquid markets.
Statistical Tests
Drift T-Test:
- Null hypothesis: No drift (mean return = 0)
- Reject if |t-stat| > threshold
- Based on standard hypothesis testing
Variance Ratio:
- Compares 2-period variance to 1-period variance
- Ratio = 1 for random walk
- Ratio < 1 for mean reversion
- Threshold of 0.8 based on empirical testing
Transition Probability Implementation
Due to Pine Script v5 limitations (no native 2D arrays), the 5×5 transition matrix is stored as a flat 1D array of 25 elements:
- Position maps to index: `row × 5 + col`
- Example: Transition from Regime 2 to Regime 4 is at index `1 × 5 + 3 = 8`
- Laplace smoothing (0.1) prevents zero probabilities
- Row sums normalized to calculate probabilities
This approach is computationally efficient and maintains statistical accuracy.
No Repainting
All calculations confirmed on bar close. Regime changes appear when the bar closes, not during formation. Historical analysis is accurate.
Alert Conditions
Regime Change
- Triggers when regime transitions to any new state
- Message shows new regime number (1-5)
Bearish Divergence
- Triggers when price makes new high but volume delta doesn't confirm
Bullish Divergence
- Triggers when price makes new low but volume delta doesn't confirm
Disclaimer
FOR EDUCATIONAL PURPOSES ONLY
This indicator uses statistical methods to analyze market regimes. It does not predict the future or guarantee trading success.
Markets are probabilistic, not deterministic. A 70% probability of staying bullish means 30% chance of regime change. Always use proper risk management.
Past regime transitions do not guarantee future transitions. Market structure can change. Statistical relationships can break down.
Never risk more than you can afford to lose. Use stop losses on every trade. Test thoroughly before live trading. Consult a qualified financial advisor.
© 2026 | Open Source
Statistical rigor meets practical application Indicator
Market Structure Break & OB Probability Toolkit [LuxAlgo]The Market Structure Break & OB Probability Toolkit indicator provides an institutional framework for identifying high-probability liquidity zones and significant market structure transitions using momentum-based filters and volume analysis.
🔶 USAGE
The indicator aims to provide a systematic approach to structural analysis, allowing traders to identify clear institutional footprints. By integrating statistical filters, the tool helps isolate high-conviction signals from market noise.
🔹 Market Structure Breaks (MSB)
Unlike standard fractal-based breaks, the MSB logic in this toolkit utilizes a Momentum Z-Score filter . This ensures that structural shifts are only highlighted when price breaks a pivot with significant conviction.
Pivot Lookback: Custom sensitivity for identifying swing highs and lows.
Volatility Filtering: Only breaks exceeding the statistical threshold are labeled, helping traders avoid low-momentum fakeouts.
🔹 Institutional Order Blocks (OB)
The script automatically detects and manages Order Blocks based on the candle preceding an MSB. Every zone includes a Point of Control (POC) line for precise entry or target consideration.
Standard OBs: Formed during structural transitions, representing potential institutional interest.
High-Probability OBs (HP-OB): Zones identified with exceptionally high impulse and volume signatures (score > 80%). These are visually distinct to highlight their increased significance.
🔹 Session Range Integration
Traders can track the ranges of the London, New York, Tokyo, and Sydney sessions. This allows for the identification of structural breaks occurring at session extremes or during high-liquidity windows.
🔹 Strategy Application
Trend Direction: Identify the prevailing bias through MSB signals. A bullish MSB followed by a retracement into a Bullish OB provides a classic institutional entry scenario.
Zone Confluence: Look for High-Probability OBs that align with Session Highs/Lows for increased trade conviction.
Re-test Analysis: Enable "Extend Broken OBs" to see how price interacts with flipped liquidity zones.
🔶 DETAILS
The toolkit utilizes several advanced logic components to maintain chart clarity and analytical depth:
Intelligent Mitigation Logic: Active zones are managed in real-time. Traders can choose between "Historical" (shows all past zones) or "Present" (shows only active zones) display modes.
Mitigated Extension: A specialized feature to extend recently broken zones, allowing for re-test analysis of formerly active liquidity.
Overlap Filter: Option to hide overlapping Order Blocks to maintain a clean, actionable chart.
🔹 Analytics Dashboard
The built-in dashboard provides a real-time performance suite:
OB Reliability: A percentage-based efficiency metric tracking how many detected zones have been successfully mitigated by price.
High-Prob Zone Count: A live counter of active HP-OBs currently remaining on the chart.
🔶 SETTINGS
🔹 Market Structure
Pivot Lookback: Defines the sensitivity of the market structure detection by adjusting the lookback period for pivots.
MSB Momentum Z-Score: Sets the statistical threshold for a price move to be considered a valid structural break.
🔹 Visuals
Display Mode: Toggles between showing historical mitigated zones or only currently active ones.
🔹 Order Blocks
Max Active OBs: Controls the maximum number of blocks stored and displayed on the chart.
Extend Broken OBs: If enabled, recently mitigated blocks will remain visible to observe potential re-tests.
Hide Overlapping OBs: Removes redundant zones that occupy the same price area as existing ones.
🔹 Sessions
Show Session Ranges: Global toggle for session visualizations.
Session Toggles: Individual controls to enable London, New York, Tokyo, or Sydney ranges with custom time and color inputs.
Institutional trading concepts and Smart Money Concept (SMC) indicators involve significant risk. This tool is designed for educational and analytical purposes. Past performance is not indicative of future results. Indicator
PineStats█ OVERVIEW
PineStats is a comprehensive statistical analysis library for Pine Script v6, providing 104 functions across 6 modules. Built for quantitative traders, researchers, and indicator developers who need professional-grade statistics without reinventing the wheel.
For building mean-reversion strategies, analyzing return distributions, measuring correlations, or testing for market regimes.
█ MODULES
CORE STATISTICS (20 functions)
• Central tendency: mean, median, WMA, EMA
• Dispersion: variance, stdev, MAD, range
• Standardization: z-score, robust z-score, normalize, percentile
• Distribution shape: skewness, kurtosis
PROBABILITY DISTRIBUTIONS (17 functions)
• Normal: PDF, CDF, inverse CDF (quantile function)
• Power-law: Hill estimator, MLE alpha, survival function
• Exponential: PDF, CDF, rate estimation
• Normality testing: Jarque-Bera test
ENTROPY (9 functions)
• Shannon entropy (information theory)
• Tsallis entropy (non-extensive, fat-tail sensitive)
• Permutation entropy (ordinal patterns)
• Approximate entropy (regularity measure)
• Entropy-based regime detection
PROBABILITY (21 functions)
• Win rates and expected value
• First passage time estimation
• TP/SL probability analysis
• Conditional probability and Bayes updates
• Streak and drawdown probabilities
REGRESSION (19 functions)
• Linear regression: slope, intercept, forecast
• Goodness of fit: R², adjusted R², standard error
• Statistical tests: t-statistic, p-value, significance
• Trend analysis: strength, angle, acceleration
• Quadratic regression
CORRELATION (18 functions)
• Pearson, Spearman, Kendall correlation
• Covariance, beta, alpha (Jensen's)
• Rolling correlation analysis
• Autocorrelation and cross-correlation
• Information ratio, tracking error
█ QUICK START
import HenriqueCentieiro/PineStats/1 as stats
// Z-score for mean reversion
z = stats.zscore(close, 20)
// Test if returns are normally distributed
returns = (close - close ) / close
isGaussian = stats.is_normal(returns, 100, 0.05)
// Regression channel
= stats.linreg_channel(close, 50, 2.0)
// Correlation with benchmark
spyReturns = request.security("SPY", timeframe.period, close/close - 1)
beta = stats.beta(returns, spyReturns, 60)
█ USE CASES
✓ Mean Reversion — z-scores, percentiles, Bollinger-style analysis
✓ Regime Detection — entropy measures, correlation regimes
✓ Risk Analysis — drawdown probability, VaR via quantiles
✓ Strategy Evaluation — expected value, win rates, R:R analysis
✓ Distribution Analysis — normality tests, fat-tail detection
✓ Multi-Asset — beta, alpha, correlation, relative strength
█ NOTES
• All functions return `na` on invalid inputs
• Designed for Pine Script v6
• Fully documented in the library header
• Part of the Pine ecosystem: PineStats, PineQuant, PineCriticality, PineWavelet
█ REFERENCES
• Abramowitz & Stegun — Normal CDF approximation
• Acklam's algorithm — Inverse normal CDF
• Hill estimator — Power-law tail estimation
• Tsallis statistics — Non-extensive entropy
Full documentation in the library header.
mean(src, length)
Calculates the arithmetic mean (simple moving average) over a lookback period
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Arithmetic mean of the last `length` values, or `na` if inputs invalid
wma_custom(src, length)
Calculates weighted moving average with linearly decreasing weights
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Weighted moving average, or `na` if inputs invalid
ema_custom(src, length)
Calculates exponential moving average
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Exponential moving average, or `na` if inputs invalid
median(src, length)
Calculates the median value over a lookback period
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Median value, or `na` if inputs invalid
variance(src, length)
Calculates population variance over a lookback period
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Population variance, or `na` if inputs invalid
stdev(src, length)
Calculates population standard deviation over a lookback period
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Population standard deviation, or `na` if inputs invalid
mad(src, length)
Calculates Median Absolute Deviation (MAD) - robust dispersion measure
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: MAD value, or `na` if inputs invalid
data_range(src, length)
Calculates the range (highest - lowest) over a lookback period
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Range value, or `na` if inputs invalid
zscore(src, length)
Calculates z-score (number of standard deviations from mean)
Parameters:
src (float) : Source series
length (simple int) : Lookback period for mean and stdev calculation (must be >= 2)
Returns: Z-score, or `na` if inputs invalid or stdev is zero
zscore_robust(src, length)
Calculates robust z-score using median and MAD (resistant to outliers)
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 2)
Returns: Robust z-score, or `na` if inputs invalid or MAD is zero
normalize(src, length)
Normalizes value to range using min-max scaling
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Normalized value in , or `na` if inputs invalid or range is zero
percentile(src, length)
Calculates percentile rank of current value within lookback window
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Percentile rank (0 to 100), or `na` if inputs invalid
winsorize(src, length, lower_pct, upper_pct)
Winsorizes values by clamping to percentile bounds (reduces outlier impact)
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
lower_pct (simple float) : Lower percentile bound (0-100, e.g., 5 for 5th percentile)
upper_pct (simple float) : Upper percentile bound (0-100, e.g., 95 for 95th percentile)
Returns: Winsorized value clamped to bounds
skewness(src, length)
Calculates sample skewness (measure of distribution asymmetry)
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 3)
Returns: Skewness value (negative = left tail, positive = right tail), or `na` if invalid
kurtosis(src, length)
Calculates excess kurtosis (measure of distribution tail heaviness)
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 4)
Returns: Excess kurtosis (>0 = heavy tails, <0 = light tails), or `na` if invalid
count_valid(src, length)
Counts non-na values in lookback window (useful for data quality checks)
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Count of valid (non-na) values
sum(src, length)
Calculates sum over lookback period
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 1)
Returns: Sum of values, or `na` if inputs invalid
cumsum(src)
Calculates cumulative sum (running total from first bar)
Parameters:
src (float) : Source series
Returns: Cumulative sum
change(src, length)
Returns the change (difference) from n bars ago
Parameters:
src (float) : Source series
length (simple int) : Number of bars to look back (must be >= 1)
Returns: Current value minus value from `length` bars ago
roc(src, length)
Calculates Rate of Change (percentage change from n bars ago)
Parameters:
src (float) : Source series
length (simple int) : Number of bars to look back (must be >= 1)
Returns: Percentage change as decimal (0.05 = 5%), or `na` if invalid
normal_pdf_standard(x)
Calculates the standard normal probability density function (PDF)
Parameters:
x (float) : The value to evaluate
Returns: PDF value at x for standard normal N(0,1)
normal_pdf(x, mu, sigma)
Calculates the normal probability density function (PDF)
Parameters:
x (float) : The value to evaluate
mu (float) : Mean of the distribution (default: 0)
sigma (float) : Standard deviation (default: 1, must be > 0)
Returns: PDF value at x for normal N(mu, sigma²)
normal_cdf_standard(x)
Calculates the standard normal cumulative distribution function (CDF)
Parameters:
x (float) : The value to evaluate
Returns: Probability P(X <= x) for standard normal N(0,1)
@description Uses Abramowitz & Stegun approximation (formula 7.1.26), accurate to ~1.5e-7
normal_cdf(x, mu, sigma)
Calculates the normal cumulative distribution function (CDF)
Parameters:
x (float) : The value to evaluate
mu (float) : Mean of the distribution (default: 0)
sigma (float) : Standard deviation (default: 1, must be > 0)
Returns: Probability P(X <= x) for normal N(mu, sigma²)
normal_inv_standard(p)
Calculates the inverse standard normal CDF (quantile function)
Parameters:
p (float) : Probability value (must be in (0, 1))
Returns: x such that P(X <= x) = p for standard normal N(0,1)
@description Uses Acklam's algorithm, accurate to ~1.15e-9
normal_inv(p, mu, sigma)
Calculates the inverse normal CDF (quantile function)
Parameters:
p (float) : Probability value (must be in (0, 1))
mu (float) : Mean of the distribution
sigma (float) : Standard deviation (must be > 0)
Returns: x such that P(X <= x) = p for normal N(mu, sigma²)
power_law_alpha(src, length, tail_pct)
Estimates power-law exponent (alpha) using Hill estimator
Parameters:
src (float) : Source series (typically absolute returns or drawdowns)
length (simple int) : Lookback period (must be >= 10 for reliable estimates)
tail_pct (simple float) : Percentage of data to use for tail estimation (default: 0.1 = top 10%)
Returns: Estimated alpha (tail index), typically 2-4 for financial data
@description Alpha < 2 indicates infinite variance (very heavy tails)
@description Alpha < 3 indicates infinite kurtosis
@description Alpha > 4 suggests near-Gaussian behavior
power_law_alpha_mle(src, length, x_min)
Estimates power-law alpha using maximum likelihood (Clauset method)
Parameters:
src (float) : Source series (positive values expected)
length (simple int) : Lookback period (must be >= 20)
x_min (float) : Minimum threshold for power-law behavior
Returns: Estimated alpha using MLE
power_law_pdf(x, alpha, x_min)
Calculates power-law probability density (Pareto Type I)
Parameters:
x (float) : Value to evaluate (must be >= x_min)
alpha (float) : Power-law exponent (must be > 1)
x_min (float) : Minimum value / scale parameter (must be > 0)
Returns: PDF value
power_law_survival(x, alpha, x_min)
Calculates power-law survival function P(X > x)
Parameters:
x (float) : Value to evaluate (must be >= x_min)
alpha (float) : Power-law exponent (must be > 1)
x_min (float) : Minimum value / scale parameter (must be > 0)
Returns: Probability of exceeding x
power_law_ks(src, length, alpha, x_min)
Tests if data follows power-law using simplified Kolmogorov-Smirnov
Parameters:
src (float) : Source series
length (simple int) : Lookback period
alpha (float) : Estimated alpha from power_law_alpha()
x_min (float) : Threshold value
Returns: KS statistic (lower = better fit, typically < 0.1 for good fit)
is_power_law(src, length, tail_pct, ks_threshold)
Simple test if distribution appears to follow power-law
Parameters:
src (float) : Source series
length (simple int) : Lookback period
tail_pct (simple float) : Tail percentage for alpha estimation
ks_threshold (simple float) : Maximum KS statistic for acceptance (default: 0.1)
Returns: true if KS test suggests power-law fit
exp_pdf(x, lambda)
Calculates exponential probability density function
Parameters:
x (float) : Value to evaluate (must be >= 0)
lambda (float) : Rate parameter (must be > 0)
Returns: PDF value
exp_cdf(x, lambda)
Calculates exponential cumulative distribution function
Parameters:
x (float) : Value to evaluate (must be >= 0)
lambda (float) : Rate parameter (must be > 0)
Returns: Probability P(X <= x)
exp_lambda(src, length)
Estimates exponential rate parameter (lambda) using MLE
Parameters:
src (float) : Source series (positive values)
length (simple int) : Lookback period
Returns: Estimated lambda (1/mean)
jarque_bera(src, length)
Calculates Jarque-Bera test statistic for normality
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 10)
Returns: JB statistic (higher = more deviation from normality)
@description Under normality, JB ~ chi-squared(2). JB > 6 suggests non-normality at 5% level
is_normal(src, length, significance)
Tests if distribution is approximately normal
Parameters:
src (float) : Source series
length (simple int) : Lookback period
significance (simple float) : Significance level (default: 0.05)
Returns: true if Jarque-Bera test does not reject normality
shannon_entropy(src, length, n_bins)
Calculates Shannon entropy from a probability distribution
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 10)
n_bins (simple int) : Number of histogram bins for discretization (default: 10)
Returns: Shannon entropy in bits (log base 2)
@description Higher entropy = more randomness/uncertainty, lower = more predictability
shannon_entropy_norm(src, length, n_bins)
Calculates normalized Shannon entropy
Parameters:
src (float) : Source series
length (simple int) : Lookback period
n_bins (simple int) : Number of histogram bins
Returns: Normalized entropy where 0 = perfectly predictable, 1 = maximum randomness
tsallis_entropy(src, length, q, n_bins)
Calculates Tsallis entropy with q-parameter
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 10)
q (float) : Entropic index (q=1 recovers Shannon entropy)
n_bins (simple int) : Number of histogram bins
Returns: Tsallis entropy value
@description q < 1: emphasizes rare events (fat tails)
@description q = 1: equivalent to Shannon entropy
@description q > 1: emphasizes common events
optimal_q(src, length)
Estimates optimal q parameter from kurtosis
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Estimated q value that best captures the distribution's tail behavior
@description Uses relationship: q ≈ (5 + kurtosis) / (3 + kurtosis) for kurtosis > 0
tsallis_q_gaussian(x, q, beta)
Calculates Tsallis q-Gaussian probability density
Parameters:
x (float) : Value to evaluate
q (float) : Tsallis q parameter (must be < 3)
beta (float) : Width parameter (inverse temperature, must be > 0)
Returns: q-Gaussian PDF value
@description q=1 recovers standard Gaussian
permutation_entropy(src, length, order)
Calculates permutation entropy (ordinal pattern complexity)
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 20)
order (simple int) : Embedding dimension / pattern length (2-5, default: 3)
Returns: Normalized permutation entropy
@description Measures complexity of temporal ordering patterns
@description 0 = perfectly predictable sequence, 1 = random
approx_entropy(src, length, m, r)
Calculates Approximate Entropy (ApEn) - regularity measure
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 50)
m (simple int) : Embedding dimension (default: 2)
r (simple float) : Tolerance as fraction of stdev (default: 0.2)
Returns: Approximate entropy value (higher = more irregular/complex)
@description Lower ApEn indicates more self-similarity and predictability
entropy_regime(src, length, q, n_bins)
Detects market regime based on entropy level
Parameters:
src (float) : Source series (typically returns)
length (simple int) : Lookback period
q (float) : Tsallis q parameter (use optimal_q() or default 1.5)
n_bins (simple int) : Number of histogram bins
Returns: Regime indicator: -1 = trending (low entropy), 0 = transition, 1 = ranging (high entropy)
entropy_risk(src, length)
Calculates entropy-based risk indicator
Parameters:
src (float) : Source series (typically returns)
length (simple int) : Lookback period
Returns: Risk score where 1 = maximum divergence from Gaussian 1
hit_rate(src, length)
Calculates hit rate (probability of positive outcome) over lookback
Parameters:
src (float) : Source series (positive values count as hits)
length (simple int) : Lookback period
Returns: Hit rate as decimal
hit_rate_cond(condition, length)
Calculates hit rate for custom condition over lookback
Parameters:
condition (bool) : Boolean series (true = hit)
length (simple int) : Lookback period
Returns: Hit rate as decimal
expected_value(src, length)
Calculates expected value of a series
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Expected value (mean)
expected_value_trade(win_prob, take_profit, stop_loss)
Calculates expected value for a trade with TP and SL levels
Parameters:
win_prob (float) : Probability of hitting TP (0-1)
take_profit (float) : Take profit in price units or %
stop_loss (float) : Stop loss in price units or % (positive value)
Returns: Expected value per trade
@description EV = (win_prob * TP) - ((1 - win_prob) * SL)
breakeven_winrate(take_profit, stop_loss)
Calculates breakeven win rate for given TP/SL ratio
Parameters:
take_profit (float) : Take profit distance
stop_loss (float) : Stop loss distance
Returns: Required win rate for breakeven (EV = 0)
reward_risk_ratio(take_profit, stop_loss)
Calculates the reward-to-risk ratio
Parameters:
take_profit (float) : Take profit distance
stop_loss (float) : Stop loss distance
Returns: R:R ratio
fpt_probability(src, length, target, max_bars)
Estimates probability of price reaching target within N bars
Parameters:
src (float) : Source series (typically returns)
length (simple int) : Lookback for volatility estimation
target (float) : Target move (in same units as src, e.g., % return)
max_bars (simple int) : Maximum bars to consider
Returns: Probability of reaching target within max_bars
@description Based on random walk with drift approximation
fpt_mean(src, length, target)
Estimates mean first passage time to target level
Parameters:
src (float) : Source series (typically returns)
length (simple int) : Lookback for volatility estimation
target (float) : Target move
Returns: Expected number of bars to reach target (can be infinite)
fpt_historical(src, length, target)
Counts historical bars to reach target from each point
Parameters:
src (float) : Source series (typically price or returns)
length (simple int) : Lookback period
target (float) : Target move from each starting point
Returns: Array of first passage times (na if target not reached within lookback)
tp_probability(src, length, tp_distance, sl_distance)
Estimates probability of hitting TP before SL
Parameters:
src (float) : Source series (typically returns)
length (simple int) : Lookback for estimation
tp_distance (float) : Take profit distance (positive)
sl_distance (float) : Stop loss distance (positive)
Returns: Probability of TP being hit first
trade_probability(src, length, tp_pct, sl_pct)
Calculates complete trade probability and EV analysis
Parameters:
src (float) : Source series (typically returns)
length (simple int) : Lookback period
tp_pct (float) : Take profit percentage
sl_pct (float) : Stop loss percentage
Returns: Tuple:
cond_prob(condition_a, condition_b, length)
Calculates conditional probability P(B|A) from historical data
Parameters:
condition_a (bool) : Condition A (the given condition)
condition_b (bool) : Condition B (the outcome)
length (simple int) : Lookback period
Returns: P(B|A) = P(A and B) / P(A)
bayes_update(prior, likelihood, false_positive)
Updates probability using Bayes' theorem
Parameters:
prior (float) : Prior probability P(H)
likelihood (float) : P(E|H) - probability of evidence given hypothesis
false_positive (float) : P(E|~H) - probability of evidence given hypothesis is false
Returns: Posterior probability P(H|E)
streak_prob(win_rate, streak_length)
Calculates probability of N consecutive wins given win rate
Parameters:
win_rate (float) : Single-trade win probability
streak_length (simple int) : Number of consecutive wins
Returns: Probability of streak
losing_streak_prob(win_rate, streak_length)
Calculates probability of experiencing N consecutive losses
Parameters:
win_rate (float) : Single-trade win probability
streak_length (simple int) : Number of consecutive losses
Returns: Probability of losing streak
drawdown_prob(src, length, dd_threshold)
Estimates probability of drawdown exceeding threshold
Parameters:
src (float) : Source series (returns)
length (simple int) : Lookback period
dd_threshold (float) : Drawdown threshold (as positive decimal, e.g., 0.10 = 10%)
Returns: Historical probability of exceeding drawdown threshold
prob_to_odds(prob)
Calculates odds from probability
Parameters:
prob (float) : Probability (0-1)
Returns: Odds (prob / (1 - prob))
odds_to_prob(odds)
Calculates probability from odds
Parameters:
odds (float) : Odds ratio
Returns: Probability (0-1)
implied_prob(decimal_odds)
Calculates implied probability from decimal odds (betting)
Parameters:
decimal_odds (float) : Decimal odds (e.g., 2.5 means $2.50 return per $1 bet)
Returns: Implied probability
logit(prob)
Calculates log-odds (logit) from probability
Parameters:
prob (float) : Probability (must be in (0, 1))
Returns: Log-odds
inv_logit(log_odds)
Calculates probability from log-odds (inverse logit / sigmoid)
Parameters:
log_odds (float) : Log-odds value
Returns: Probability (0-1)
linreg_slope(src, length)
Calculates linear regression slope
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 2)
Returns: Slope coefficient (change per bar)
linreg_intercept(src, length)
Calculates linear regression intercept
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 2)
Returns: Intercept (predicted value at oldest bar in window)
linreg_value(src, length)
Calculates predicted value at current bar using linear regression
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Predicted value at current bar (end of regression line)
linreg_forecast(src, length, offset)
Forecasts value N bars ahead using linear regression
Parameters:
src (float) : Source series
length (simple int) : Lookback period for regression
offset (simple int) : Bars ahead to forecast (positive = future)
Returns: Forecasted value
linreg_channel(src, length, mult)
Calculates linear regression channel with bands
Parameters:
src (float) : Source series
length (simple int) : Lookback period
mult (simple float) : Standard deviation multiplier for bands
Returns: Tuple:
r_squared(src, length)
Calculates R-squared (coefficient of determination)
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: R² value where 1 = perfect linear fit
adj_r_squared(src, length)
Calculates adjusted R-squared (accounts for sample size)
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Adjusted R² value
std_error(src, length)
Calculates standard error of estimate (residual standard deviation)
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Standard error
residual(src, length)
Calculates residual at current bar
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Residual (actual - predicted)
residuals(src, length)
Returns array of all residuals in lookback window
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Array of residuals
t_statistic(src, length)
Calculates t-statistic for slope coefficient
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: T-statistic (slope / standard error of slope)
slope_pvalue(src, length)
Approximates p-value for slope t-test (two-tailed)
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Approximate p-value
is_significant(src, length, alpha)
Tests if regression slope is statistically significant
Parameters:
src (float) : Source series
length (simple int) : Lookback period
alpha (simple float) : Significance level (default: 0.05)
Returns: true if slope is significant at alpha level
trend_strength(src, length)
Calculates normalized trend strength based on R² and slope
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Trend strength where sign indicates direction
trend_angle(src, length)
Calculates trend angle in degrees
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Angle in degrees (positive = uptrend, negative = downtrend)
linreg_acceleration(src, length)
Calculates trend acceleration (second derivative)
Parameters:
src (float) : Source series
length (simple int) : Lookback period for each regression
Returns: Acceleration (change in slope)
linreg_deviation(src, length)
Calculates deviation from regression line in standard error units
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Deviation in standard error units (like z-score)
quadreg_coefficients(src, length)
Fits quadratic regression and returns coefficients
Parameters:
src (float) : Source series
length (simple int) : Lookback period (must be >= 4)
Returns: Tuple: for y = a*x² + b*x + c
quadreg_value(src, length)
Calculates quadratic regression value at current bar
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: Predicted value from quadratic fit
correlation(x, y, length)
Calculates Pearson correlation coefficient between two series
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period (must be >= 3)
Returns: Correlation coefficient
covariance(x, y, length)
Calculates sample covariance between two series
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period (must be >= 2)
Returns: Covariance value
beta(asset, benchmark, length)
Calculates beta coefficient (slope of regression of y on x)
Parameters:
asset (float) : Asset returns series
benchmark (float) : Benchmark returns series
length (simple int) : Lookback period
Returns: Beta coefficient
@description Beta = Cov(asset, benchmark) / Var(benchmark)
alpha(asset, benchmark, length, risk_free)
Calculates alpha (Jensen's alpha / intercept)
Parameters:
asset (float) : Asset returns series
benchmark (float) : Benchmark returns series
length (simple int) : Lookback period
risk_free (float) : Risk-free rate (default: 0)
Returns: Alpha value (excess return not explained by beta)
spearman(x, y, length)
Calculates Spearman rank correlation coefficient
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period (must be >= 3)
Returns: Spearman correlation
@description More robust to outliers than Pearson correlation
kendall_tau(x, y, length)
Calculates Kendall's tau rank correlation (simplified)
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period (must be >= 3)
Returns: Kendall's tau
correlation_change(x, y, length, change_period)
Calculates change in correlation over time
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period for correlation
change_period (simple int) : Period over which to measure change
Returns: Change in correlation
correlation_regime(x, y, length, ma_length)
Detects correlation regime based on level and stability
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period for correlation
ma_length (simple int) : Moving average length for smoothing
Returns: Regime: -1 = negative, 0 = uncorrelated, 1 = positive
correlation_stability(x, y, length, stability_length)
Calculates correlation stability (inverse of volatility)
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback for correlation
stability_length (simple int) : Lookback for stability calculation
Returns: Stability score where 1 = perfectly stable
relative_strength(asset, benchmark, length)
Calculates relative strength of asset vs benchmark
Parameters:
asset (float) : Asset price series
benchmark (float) : Benchmark price series
length (simple int) : Smoothing period
Returns: Relative strength ratio (normalized)
tracking_error(asset, benchmark, length)
Calculates tracking error (standard deviation of excess returns)
Parameters:
asset (float) : Asset returns
benchmark (float) : Benchmark returns
length (simple int) : Lookback period
Returns: Tracking error (annualize by multiplying by sqrt(252) for daily data)
information_ratio(asset, benchmark, length)
Calculates information ratio (risk-adjusted excess return)
Parameters:
asset (float) : Asset returns
benchmark (float) : Benchmark returns
length (simple int) : Lookback period
Returns: Information ratio
capture_ratio(asset, benchmark, length, up_capture)
Calculates up/down capture ratio
Parameters:
asset (float) : Asset returns
benchmark (float) : Benchmark returns
length (simple int) : Lookback period
up_capture (simple bool) : If true, calculate up capture; if false, down capture
Returns: Capture ratio
autocorrelation(src, length, lag)
Calculates autocorrelation at specified lag
Parameters:
src (float) : Source series
length (simple int) : Lookback period
lag (simple int) : Lag for autocorrelation (default: 1)
Returns: Autocorrelation at specified lag
partial_autocorr(src, length)
Calculates partial autocorrelation at lag 1
Parameters:
src (float) : Source series
length (simple int) : Lookback period
Returns: PACF at lag 1 (equals ACF at lag 1)
autocorr_test(src, length, max_lag)
Tests for significant autocorrelation (Ljung-Box inspired)
Parameters:
src (float) : Source series
length (simple int) : Lookback period
max_lag (simple int) : Maximum lag to test
Returns: Sum of squared autocorrelations (higher = more autocorrelation)
cross_correlation(x, y, length, lag)
Calculates cross-correlation at specified lag
Parameters:
x (float) : First series
y (float) : Second series (lagged)
length (simple int) : Lookback period
lag (simple int) : Lag to apply to y (positive = y leads x)
Returns: Cross-correlation at specified lag
cross_correlation_peak(x, y, length, max_lag)
Finds lag with maximum cross-correlation
Parameters:
x (float) : First series
y (float) : Second series
length (simple int) : Lookback period
max_lag (simple int) : Maximum lag to search (both directions)
Returns: Tuple: Library
Advanced Momentum TrackerThe Advanced Momentum Tracker (AMT) is a technical indicator designed to identify high-probability trend reversals and momentum shifts in real-time. Unlike traditional indicators that rely solely on mathematical formulas, AMT analyzes price action structure and historical patterns to detect when market momentum is shifting from bullish to bearish (and vice versa).
Core Methodology:
The indicator tracks consecutive price movements and maintains a comprehensive database of historical momentum patterns. It identifies trend changes by analyzing:
Sequential candle relationships (opens and closes)
Break of key trailing stop levels formed by recent price action
Historical success rates of similar momentum patterns
Key Features
1. Dynamic Levels:
Automatically plots real-time dynamic trailing stop levels based on current momentum
Color-coded lines: Green for bullish momentum, Red for bearish momentum
These levels act as trigger points for potential trend changes
2. Entry Signal Markers:
Clear BUY (↑) and SELL (↓) arrows when momentum shifts are detected
Arrows positioned above/below candles for maximum visibility ,Signals only appear on confirmed trend changes
3. Momentum Score Display:
Shows statistical probability based on historical pattern analysis
Displays strength percentage of current momentum continuation
Helps traders assess confidence level of the current trend
4. Exit Zone Indicator:
Plots recommended exit levels for active positions
Dynamic color coding: Red for long exits, Green for short exits
Warning system (orange) when price breaches exit zones
5. Position Management Filter:
Optional risk filter to avoid trades with excessive distance from trigger level
Customizable position threshold percentage
Helps maintain consistent risk-reward ratios
6. Comprehensive Alert System:
Customizable alert messages for both long and short signals
Configurable alert frequency (once per bar or once per bar close)
Real-time notifications for all signal types
Customization Options-
Visual Settings:
Toggle visibility of current price level, momentum score, and exit zones
Customizable colors for all elements (bullish/bearish themes)
Adjustable line thickness for dynamic levels
Entry Markers:
Custom colors for long and short entry signals
Adjustable arrow distance from candles
Core Parameters:
Historical Depth: Amount of past data to analyze (default: 20,000 bars)
Sensitivity Level: Controls how strong a move must be to trigger signals (default: 4)
Higher values = fewer but stronger signals
Lower values = more signals with earlier entries
Position Management:
Enable/disable position filter
Set maximum acceptable risk threshold as percentage
How It Works:-
Momentum Detection Engine: The script continuously monitors price action, tracking each bullish and bearish leg. It maintains arrays of opens, closes, and counts to build a comprehensive picture of market structure.
Pattern Recognition: When price breaks key levels (minimum/maximum of recent candles based on sensitivity), the indicator recognizes a potential momentum shift.
Statistical Validation: The script compares the current pattern against its historical database to calculate the probability of momentum continuation.
Signal Generation: When a valid trend change is detected (and passes the position filter if enabled), entry signals are displayed with corresponding exit zones.
Best Use Cases:
Swing trading on any timeframe (works on 1m to 1D charts)
Trend reversal identification
Momentum trading strategies
Works on all markets: Forex, Stocks, Crypto, Indices, Commodities etc
Recommended Settings:
Scalping/Day Trading: Sensitivity 2-3, Historical Depth 10,000-20,000
Swing Trading: Sensitivity 3-4, Historical Depth 20,000-30,000
Position Trading: Sensitivity 4-5, Historical Depth 30,000+
Important Notes:
Signals appear only on confirmed bars (not on real-time candles unless confirmed)
The momentum score becomes more accurate as more historical data is processed
Position filter should be adjusted based on the volatility of the instrument being traded
Best used in conjunction with proper risk management and position sizing
What Makes This Indicator Unique:
Unlike indicators that simply apply mathematical formulas to price data, AMT learns from historical price behavior. It doesn't just tell you what happened—it tells you what's likely to happen next based on thousands of similar situations in the past. The statistical momentum score provides an edge that pure technical indicators cannot offer.
Disclaimer: This indicator is a tool for technical analysis and should not be used as the sole basis for trading decisions. Always use proper risk management and combine with your own analysis. Happy Trading !! Indicator
Probability-Based Adaptive Detection🙏🏻 PBAD (Probability-Based Adaptive Detection) : adaptive control tool for outliers || novelty detection, made for worst case data & processes, for the highest time complexity O(n^2) compared with the alternatives (would be explained in a sec). Thresholds are completely data driven and axiomatic, no need in provided hyperparameters, are not learned or optimized. The method accepts multiple weights, e.g. both temporal and volatility weights.
Method briefly explained (I can go deeper if any1 asks explicitly):
Performs weighted KDE on initial input data, finds KDE global maximum (mode), creates new “residuals” dataset by centering initial data around this value;
Performs weighted KDE on residuals, uses sigmoid based probability mass targets with increasing probability coverage to construct a set of non-disjoint High Density Intervals (also called HDR, HPD in Bayesian terms);
Uses these intervals to calculate analogs of centralized & standardized moments;
Uses these ^^ moments to construct a set of control thresholds. The scheme used in PBAD is not only based on a central threshold, or on neighboring ones, it utilizes all previous thresholds, gaining more information.
...
The most important part is to understand whether you really need PBAD. Because even tho it seems to be the best one given highest algocomplexity, irl it would work worse in cases when it’s not required by your data.
Here’s the menu (aka taxonomy omg) of methods you can use that would let you make the right choice:
Moment-Based Adaptive Detection (MBAD) :
Norm: L2
Time complexity: original O(n), successfully reduced to O(1) in online version
Use case: default, general purpose
Based on: method of moments (powers of residuals from mean)
Thresholds architecture: centralized
Quantile-Based Adaptive Detection (QBAD):
Norm: L1
Time complexity: O(nlogn)
Use case: either bad data Or process instability
Based on: quantile moments (dyadic percentiles of residuals from median)
Thresholds architecture: chained/recursive/sequential
Probability-Based Adaptive Detection (PBAD):
Norm: L0
Time complexity: O(n^2)
Use case: both bad data And process instability
Based on: probability moments (target probability masses of residuals from KDE mode)
Thresholds architecture: decentralized (for lack of a better name xd, the idea is that these thresholds gain information from the all other threshold and are Not exclusively based on the central or neighboring thresholds)
...
Examples of true use cases:
^^ an appropriate financial instrument to use PBAD
^^ and another one
...
Additional details about how to use it:
Keep the student5 kernel, it’s the best you can do. I added others mostly for comparisons and if you want to use the tool Not for its primary purpose (on a fine data)
“Calculate for N bars” and “Starting at bar N” options allow to reduce calculation period only on the N number of last bars or next bars from a chosen one. It's vital, because calculations here are heavy
Keep plotting offset at 1 (allows to visually compare current bar with the previous threshold values). This is the way it should be done on price data.
HLC3 is the optimal source input, unless you want to use your own better one point estimate of each datapoint (in the best case done by using PBAD itself on OHLC+ values).
In essence it should be used just like MBAD or QBAD, fade/push extensions and limit, fade/push/skip deviations & basis, or other strategies of your. Again, the only reason for 3 methods to exist is to be chosen for according data characteristics.
Btw:
This is the initial version, I don’t consider it perfected tbh, even tho it works as expected, however this method is very situational anyways.
In this script KDE function is modified to ensure the outcoming probabilities Do sum up to 1. I didn’t do this normalization in Weighted KDE Mode script , but there it’s not required since we just need a KDE global max.
see ya
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Indicator
Session ATR Progression Tracker📊 Session ATR Progression Tracker - SIYL Regression Trading Tool
Track how much of your instrument's 7-day Average True Range (ATR) has been covered during the current trading session. This indicator is specifically designed for regression traders who follow the "Stay In Your Lane" (SIYL) methodology, helping you identify when the probability of mean reversion significantly increases. If you are interested in more on that check out Rod Casselli and tradersdevgroup.com.
🎯 Key Features:
• Real-time ATR Coverage Percentage - See at a glance what percentage of the 7-day ATR has been covered in the current session
• SIYL-Optimized Thresholds - See at a glance when the instrument has achieved 80% and 100% ATR coverage, the proven thresholds where mean reversion probability increases (customizable)
• Flexible Session Modes:
- Daily: Resets at calendar day change
- Session: Uses exchange-defined trading sessions
- Custom Session: Set your exact session start/end times (perfect for futures traders and international markets)
• Visual Alerts - Color-coded display (gray → orange → red) and optional background highlighting
• Repositionable Display - Choose from 9 screen positions to avoid chart clutter
• Session Markers - Green triangles mark the start of each new session
• Detailed Stats - View current range, ATR value, session high/low, and session status
💡 Why Use This Indicator?
This tool is built around a proven concept: regression trading becomes significantly more effective once a session has achieved at least 80% of its 7-day ATR. At this threshold, the probability of price reverting to mean increases substantially, creating higher-probability trade setups for SIYL practitioners.
Benefits for regression traders:
- Identify optimal entry points when mean reversion probability is highest (≥80% ATR coverage)
- Avoid premature regression entries before adequate range has been established
- Recognize when daily moves have "earned their range" and are ripe for reversal
- Time fade-the-move and counter-trend strategies with statistical backing
- Improve win rates by trading only after proven probability thresholds are met
⚙️ Setup Instructions:
1. Add the indicator to your chart
2. Select your preferred "Reset Mode" (recommend "Custom Session" for futures/international markets)
3. If using Custom Session, enter your session times in 24-hour format (e.g., 0930-1600 for US stocks, 1700-1600 for CME futures)
4. Adjust alert thresholds if desired (default: 80% and 100% - proven SIYL thresholds)
5. Position the display where it's most visible on your chart
📈 Works Across All Markets:
Stocks • Futures • Forex • Indices • Crypto • Commodities
Perfect for regression traders, mean reversion specialists, and SIYL practitioners who want to trade with probability on their side by entering only after the session has "earned its range."
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Tip: For futures contracts with overnight sessions that span calendar days (like MES, MNQ, MYM), use "Custom Session" mode with your exchange's official session times for accurate tracking.
Indicator
SMC N-Gram Probability Matrix [PhenLabs]📊 SMC N-Gram Probability Matrix
Version: PineScript™ v6
📌 Description
The SMC N-Gram Probability Matrix applies computational linguistics methodology to Smart Money Concepts trading. By treating SMC patterns as a discrete “alphabet” and analyzing their sequential relationships through N-gram modeling, this indicator calculates the statistical probability of which pattern will appear next based on historical transitions.
Traditional SMC analysis is reactive—traders identify patterns after they form and then anticipate the next move. This indicator inverts that approach by building a transition probability matrix from up to 5,000 bars of pattern history, enabling traders to see which SMC formations most frequently follow their current market sequence.
The indicator detects and classifies 11 distinct SMC patterns including Fair Value Gaps, Order Blocks, Liquidity Sweeps, Break of Structure, and Change of Character in both bullish and bearish variants, then tracks how these patterns transition from one to another over time.
🚀 Points of Innovation
First indicator to apply N-gram sequence modeling from computational linguistics to SMC pattern analysis
Dynamic transition matrix rebuilds every 50 bars for adaptive probability calculations
Supports bigram (2), trigram (3), and quadgram (4) sequence lengths for varying analysis depth
Priority-based pattern classification ensures higher-significance patterns (CHoCH, BOS) take precedence
Configurable minimum occurrence threshold filters out statistically insignificant predictions
Real-time probability visualization with graphical confidence bars
🔧 Core Components
Pattern Alphabet System: 11 discrete SMC patterns encoded as integers for efficient matrix indexing and transition tracking
Swing Point Detection: Uses ta.pivothigh/pivotlow with configurable sensitivity for non-repainting structure identification
Transition Count Matrix: Flattened array storing occurrence counts for all possible pattern sequence transitions
Context Encoder: Converts N-gram pattern sequences into unique integer IDs for matrix lookup
Probability Calculator: Transforms raw transition counts into percentage probabilities for each possible next pattern
🔥 Key Features
Multi-Pattern SMC Detection: Simultaneously identifies FVGs, Order Blocks, Liquidity Sweeps, BOS, and CHoCH formations
Adjustable N-Gram Length: Choose between 2-4 pattern sequences to balance specificity against sample size
Flexible Lookback Range: Analyze anywhere from 100 to 5,000 historical bars for matrix construction
Pattern Toggle Controls: Enable or disable individual SMC pattern types to customize analysis focus
Probability Threshold Filtering: Set minimum occurrence requirements to ensure prediction reliability
Alert Integration: Built-in alert conditions trigger when high-probability predictions emerge
🎨 Visualization
Probability Table: Displays current pattern, recent sequence, sample count, and top N predicted patterns with percentage probabilities
Graphical Probability Bars: Visual bar representation (█░) showing relative probability strength at a glance
Chart Pattern Markers: Color-coded labels placed directly on price bars identifying detected SMC formations
Pattern Short Codes: Compact notation (F+, F-, O+, O-, L↑, L↓, B+, B-, C+, C-) for quick pattern identification
Customizable Table Position: Place probability display in any corner of your chart
📖 Usage Guidelines
N-Gram Configuration
N-Gram Length: Default 2, Range 2-4. Lower values provide more samples but less specificity. Higher values capture complex sequences but require more historical data.
Matrix Lookback Bars: Default 500, Range 100-5000. More bars increase statistical significance but may include outdated market behavior.
Min Occurrences for Prediction: Default 2, Range 1-10. Higher values filter noise but may reduce prediction availability.
SMC Detection Settings
Swing Detection Length: Default 5, Range 2-20. Controls pivot sensitivity for structure analysis.
FVG Minimum Size: Default 0.1%, Range 0.01-2.0%. Filters insignificant gaps.
Order Block Lookback: Default 10, Range 3-30. Bars to search for OB formations.
Liquidity Sweep Threshold: Default 0.3%, Range 0.05-1.0%. Minimum wick extension beyond swing points.
Display Settings
Show Probability Table: Toggle the probability matrix display on/off.
Show Top N Probabilities: Default 5, Range 3-10. Number of predicted patterns to display.
Show SMC Markers: Toggle on-chart pattern labels.
✅ Best Use Cases
Anticipating continuation or reversal patterns after liquidity sweeps
Identifying high-probability BOS/CHoCH sequences for trend trading
Filtering FVG and Order Block signals based on historical follow-through rates
Building confluence by comparing predicted patterns with other technical analysis
Studying how SMC patterns typically sequence on specific instruments or timeframes
⚠️ Limitations
Predictions are based solely on historical pattern frequency and do not account for fundamental factors
Low sample counts produce unreliable probabilities—always check the Samples display
Market regime changes can invalidate historical transition patterns
The indicator requires sufficient historical data to build meaningful probability matrices
Pattern detection uses standardized parameters that may not capture all institutional activity
💡 What Makes This Unique
Linguistic Modeling Applied to Markets: Treats SMC patterns like words in a language, analyzing how they “flow” together
Quantified Pattern Relationships: Transforms subjective SMC analysis into objective probability percentages
Adaptive Learning: Matrix rebuilds periodically to incorporate recent pattern behavior
Comprehensive SMC Coverage: Tracks all major Smart Money Concepts in a unified probability framework
🔬 How It Works
1. Pattern Detection Phase
Each bar is analyzed for SMC formations using configurable detection parameters
A priority hierarchy assigns the most significant pattern when multiple detections occur
2. Sequence Encoding Phase
Detected patterns are stored in a rolling history buffer of recent classifications
The current N-gram context is encoded into a unique integer identifier
3. Matrix Construction Phase
Historical pattern sequences are iterated to count transition occurrences
Each context-to-next-pattern transition increments the appropriate matrix cell
4. Probability Calculation Phase
Current context ID retrieves corresponding transition counts from the matrix
Raw counts are converted to percentages based on total context occurrences
5. Visualization Phase
Probabilities are sorted and the top N predictions are displayed in the table
Chart markers identify the current detected pattern for visual reference
💡 Note:
This indicator performs best when used as a confluence tool alongside traditional SMC analysis. The probability predictions highlight statistically common pattern sequences but should not be used as standalone trading signals. Always verify predictions against price action context, higher timeframe structure, and your overall trading plan. Monitor the sample count to ensure predictions are based on adequate historical data. Indicator
Per Bak Self-Organized CriticalityTL;DR: This indicator measures market fragility. It measures the system's vulnerability to cascade failures and phase transitions. I've added four independent stress vectors: tail risk, volatility regime, credit stress, and positioning extremes. This allows us to quantify how susceptible markets are to disproportionate moves from small shocks, similar to how a steep sandpile is primed for avalanches.
Avalanches, forest fires, earthquakes, pandemic outbreaks, and market crashes. What do they all have in common? They are not random.
These events follow power laws - stable systems that naturally evolve toward critical states where small triggers can unleash catastrophic cascades.
For example, if you are building a sandpile, there will be a point with a little bit additional sand will cause a landslide.
Markets build fragility grain by grain, like a sandpile approaching avalanche.
The Per Bak Self-Organized Criticality (SOC) indicator detects when the markets are a few grains away from collapse.
This indicator is highly inspired by the work of Per Bak related to the science of self-organized criticality .
As Bak said:
"The earthquake does not 'know how large it will become'. Thus, any precursor state of a large event is essentially identical to a precursor state of a small event."
For markets, this means:
We cannot predict individual crash size from initial conditions
We can predict statistical distribution of crashes
We can identify periods of increased systemic risk (proximity to critical state)
BTW, this is a forwarding looking indicator and doesn't reprint. :)
The Story of Per Bak
In 1987, Danish physicist Per Bak and his colleagues discovered an important pattern in nature: self-organized criticality.
Their sandpile experiment revealed something: drop grains of sand one by one onto a pile, and the system naturally evolves toward a critical state. Most grains cause nothing. Some trigger small slides. But occasionally a single grain triggers a massive avalanche.
The key insight is that we cannot predict which grain will trigger the avalanche, but you can measure when the pile has reached a critical state.
Why Markets Are the Ultimate SOC System?
Financial markets exhibit all the hallmarks of self-organized criticality:
Interconnected agents (traders, institutions, algorithms) with feedback loops
Non-linear interactions where small events can cascade through the system
Power-law distributions of returns (fat tails, not normal distributions)
Natural evolution toward fragility as leverage builds, correlations tighten, and positioning crowds
Phase transitions where calm markets suddenly shift to crisis regimes
Mathematical Foundation
Power Law Distributions
Traditional finance assumes returns follow a normal distribution. "Markets return 10% on average." But I disagree. Markets follow power laws:
P(x) ∝ x^(-α)
Where P(x) is the probability of an event of size x, and α is the power law exponent (typically 3-4 for financial markets).
What this means: Small moves happen constantly. Medium moves are less frequent. Catastrophic moves are rare but follow predictable probability distributions. The "fat tails" are features of critical systems.
Critical Slowing Down
As systems approach phase transitions, they exhibit critical slowing down—reduced ability to absorb shocks. Mathematically, this appears as:
τ ∝ |T - T_c|^(-ν)
Where τ is the relaxation time, T is the current state, T_c is the critical threshold, and ν is the critical exponent.
Translation: Near criticality, markets take longer to recover from perturbations. Fragility compounds.
Component Aggregation & Non-Linear Emergence
The Per Bak SOC our index aggregates four normalized components (each scaled 0-100) with tunable weights:
SOC = w₁·C_tail + w₂·C_vol + w₃·C_credit + w₄·C_position
Default weights (you can change this):
w₁ = 0.34 (Tail Risk via SKEW)
w₂ = 0.26 (Volatility Regime via VIX term structure)
w₃ = 0.18 (Credit Stress via HYG/LQD + TED spread)
w₄ = 0.22 (Positioning Extremes via Put/Call ratio)
Each component uses percentile ranking over a 252-day lookback combined with absolute thresholds to capture both relative regime shifts and extreme absolute levels.
The Four Pillars Explained
1. Tail Risk (SKEW Index)
Measures options market pricing of fat-tail events. High SKEW indicates elevated outlier probability.
C_tail = 0.7·percentrank(SKEW, 252) + 0.3·((SKEW - 115)/0.5)
2. Volatility Regime (VIX Term Structure)
Combines VIX level with term structure slope. Backwardation signals acute stress.
C_vol = 0.4·VIX_level + 0.35·VIX_slope + 0.25·VIX_ratio
3. Credit Stress (HYG/LQD + TED Spread)
Tracks high-yield deterioration versus investment-grade and interbank lending stress.
C_credit = 0.65·percentrank(LQD/HYG, 252) + 0.35·(TED/0.75)·100
4. Positioning Extremes (Put/Call Ratio)
Detects extreme hedging demand through percentile ranking and z-score analysis.
C_position = 0.6·percentrank(P/C, 252) + 0.4·zscore_normalized
What the Indicator Really Measures?
Not Volatility but Fragility
Markets Going Down ≠ Fragility Building (actually when markets go down, risk and fragility are released)
The 0-100 Scale & Regime Thresholds
The indicator outputs a 0-100 fragility score with four regimes:
🟢 Safe (0-39): System resilient, can absorb normal shocks
🟡 Building (40-54): Early fragility signs, watch for deterioration
🟠 Elevated (55-69): System vulnerable
🔴 Critical (70-100): Highly susceptible to cascade failures
Further Reading for Nerds
Bak, P., Tang, C., & Wiesenfeld, K. (1987). "Self-organized criticality: An explanation of 1/f noise." Physical Review Letters.
Bak, P. & Chen, K. (1991). "Self-organized criticality." Scientific American.
Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. Copernicus.
Feedback is appreciated :) Indicator
Weighted KDE Mode🙏🏻 The ‘ultimate’ typical value estimator, for the highest computational cost @ time complexity O(n^2). I am not afraid to say: this is the last resort BFG9000 you can ‘ever’ get to make dem market demons kneel before y’all
Quickguide
pls read it, you won’t find it anywhere else in open access
When to use:
If current market activity is so crazy || things on your charts are really so bad (contaminated data && (data has very heavy tails || very pronounced peak)), the only option left is to use the peak (mode) of Kernel Density Estimate , instead of median not even mentioning mean. So when WMA won’t help, when WPNR won’t help, you need this thing.
Setting it up:
Interval: choose what u need, you can use usual moving windows, but I also added yearly and session anchors alike in old VWAP (always prefer 24h instead of Session if your plan allows). Other options like cumulative window are also there.
Parameters: this script ain't no joke, it needs time to make calculations, so I added a setting to calculate only for the last N bars (when “starting at bar N” is put on 0). If it’s not zero it acts as a starting point after which the calculations happen (useful for backtesting). Other parameters keep em as they are, keep student5 kernel , turn off appropriate weights if u apply it to other than chart data, on other studies etc.
But instead of listening to me just experiment with parameters and see what they change, would take 5 mins max
Been always saying that VWAP is ish, not time-aware etc, volume info is incorporated in a lil bit wrong way… So I decided not just to fix VWAP (you can do it yourself in 5 mins), but instead to drop there the Ultimate xD typical value estimator that is ever possible to do. Time aware, volume / inferred volume aware, resistant to all kinds of BS. This is your shieldwall.
How it works:
You can easily do a weighted kernel density estimation, in our case including temporal and intensity information while accumulating densities. Here are some details worth mentioning about the thing:
Kernels are raw (not unit variance), that’s easier to work with later.
h_constants for each kernel were calculated ^^ given that ^^ with python mpmath module with high decimal precision.
In bandwidth calculation instead of using empirical standard deviation as a scaler, I use... ta.range(src, len) / math.sqrt(12)
...that takes data range and converts it to standard deviation, assuming data is uniformly distributed. That’s exactly what we need: a scaler that is coherent with the KDE, that has nothing to do with stdevs, as the kernels except for gaussian ones (that we don’t even need to use). More importantly, if u take multiple windows and see over time which distro they approach on the long term, that would be the uniform one (not the normal one as many think). Sometimes windows are multimodal, sometimes Laplace like etc, so in general all together they are uniform ish.
The one and only kernel you really need is Student t with v = 5 , for the use case I highlighted in the first part of the post for TV users. It’s as far as u can get until ish becomes crazy like undefined variance etc. It has the highest kurtosis = 9 of all distros, perfect for the real use case I mentioned. Otherwise, you don’t even need KDE 4 real, but still I included other senseful kernels for comparison or in case I am trippin there.
Btw, don’t believe in all that hype about Epanechnikov kernel which in essence is made from beta distribution with alpha = beta = 2, idk why folk call it with that weird name, it’s beta2 kernel. Yes on papers it really minimises AMISE (that’s how I calculated h constants for all dem kernels in the script), but for really crazy data (proper use case for us), it ain't provides even ‘closely’ compared with student5 kernel. Not much else to add.
Shout out to @RicardoSantos for inspiration, I saw your KDE script a long time ago brotha, finna got my hands on it.
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Indicator
Indicator
First Passage Time - Distribution AnalysisThe First Passage Time (FPT) Distribution Analysis indicator is a sophisticated probabilistic tool that answers one of the most critical questions in trading: "How long will it take for price to reach my target, and what are the odds of getting there first?"
Unlike traditional technical indicators that focus on what might happen, this indicator tells you when it's likely to happen.
Mathematical Foundation: First Passage Time Theory
What is First Passage Time?
First Passage Time (FPT) is a concept in stochastic processes that measures the time it takes for a random process to reach a specific threshold for the first time. Originally developed in physics and mathematics, FPT has applications in:
Quantitative Finance: Option pricing, risk management, and algorithmic trading
Neuroscience: Modeling neural firing patterns
Biology: Population dynamics and disease spread
Engineering: Reliability analysis and failure prediction
The Mathematics Behind It
This indicator uses Geometric Brownian Motion (GBM), the same stochastic model used in the Black-Scholes option pricing formula:
dS = μS dt + σS dW
Where:
S = Asset price
μ = Drift (trend component)
σ = Volatility (uncertainty component)
dW = Wiener process (random walk)
Through Monte Carlo simulation, the indicator runs 1,000+ price path simulations to statistically determine:
When each threshold (+X% or -X%) is likely to be hit
Which threshold is hit first (directional bias)
How often each scenario occurs (probability distribution)
🎯 How This Indicator Works
Core Algorithm Workflow:
Calculate Historical Statistics
Measures recent price volatility (standard deviation of log returns)
Calculates drift (average directional movement)
Annualizes these metrics for meaningful comparison
Run Monte Carlo Simulations
Generates 1,000+ random price paths based on historical behavior
Tracks when each path hits the upside (+X%) or downside (-X%) threshold
Records which threshold was hit first in each simulation
Aggregate Statistical Results
Calculates percentile distributions (10th, 25th, 50th, 75th, 90th)
Computes "first hit" probabilities (upside vs downside)
Determines average and median time-to-target
Visual Representation
Displays thresholds as horizontal lines
Shows gradient risk zones (purple-to-blue)
Provides comprehensive statistics table
📈 Use Cases
1. Options Trading
Selling Options: Determine if your strike price is likely to be hit before expiration
Buying Options: Estimate probability of reaching profit targets within your time window
Time Decay Management: Compare expected time-to-target vs theta decay
Example: You're considering selling a 30-day call option 5% out of the money. The indicator shows there's a 72% chance price hits +5% within 12 days. This tells you the trade has high assignment risk.
2. Swing Trading
Entry Timing: Wait for higher probability setups when directional bias is strong
Target Setting: Use median time-to-target to set realistic profit expectations
Stop Loss Placement: Understand probability of hitting your stop before target
Example: The indicator shows 85% upside probability with median time of 3.2 days. You can confidently enter long positions with appropriate position sizing.
3. Risk Management
Position Sizing: Larger positions when probability heavily favors one direction
Portfolio Allocation: Reduce exposure when probabilities are near 50/50 (high uncertainty)
Hedge Timing: Know when to add protective positions based on downside probability
Example: Indicator shows 55% upside vs 45% downside—nearly neutral. This signals high uncertainty, suggesting reduced position size or wait for better setup.
4. Market Regime Detection
Trending Markets: High directional bias (70%+ one direction)
Range-bound Markets: Balanced probabilities (45-55% both directions)
Volatility Regimes: Compare actual vs theoretical minimum time
Example: Consistent 90%+ bullish bias across multiple timeframes confirms strong uptrend—stay long and avoid counter-trend trades.
First Hit Rate (Most Important!)
Shows which threshold is likely to be hit FIRST:
Upside %: Probability of hitting upside target before downside
Downside %: Probability of hitting downside target before upside
These always sum to 100%
⚠️ Warning: If you see "Low Hit Rate" warning, increase this parameter!
Advanced Parameters
Drift Mode
Allows you to explore different scenarios:
Historical: Uses actual recent trend (default—most realistic)
Zero (Neutral): Assumes no trend, only volatility (symmetric probabilities)
50% Reduced: Dampens trend effect (conservative scenario)
Use Case: Switch to "Zero (Neutral)" to see what happens in a pure volatility environment, useful for range-bound markets.
Distribution Type
Percentile: Shows 10%, 25%, 50%, 75%, 90% levels (recommended for most users)
Sigma: Shows standard deviation levels (1σ, 2σ)—useful for statistical analysis
⚠️ Important Limitations & Best Practices
Limitations
Assumes GBM: Real markets have fat tails, jumps, and regime changes not captured by GBM
Historical Parameters: Uses recent volatility/drift—may not predict regime shifts
No Fundamental Events: Cannot predict earnings, news, or macro shocks
Computational: Runs only on last bar—doesn't give historical signals
Remember: Probabilities are not certainties. Use this indicator as part of a comprehensive trading plan with proper risk management.
Created by: Henrique Centieiro. feedback is more than welcome! Indicator
Indicator
Institutional Levels (CNN) - [PhenLabs]📊Institutional Levels (Convolutional Neural Network-inspired)
Version : PineScript™v6
📌Description
The CNN-IL Institutional Levels indicator represents a breakthrough in automated zone detection technology, combining convolutional neural network principles with advanced statistical modeling. This sophisticated tool identifies high-probability institutional trading zones by analyzing pivot patterns, volume dynamics, and price behavior using machine learning algorithms.
The indicator employs a proprietary 9-factor logistic regression model that calculates real-time reaction probabilities for each detected zone. By incorporating CNN-inspired filtering techniques and dynamic zone management, it provides traders with unprecedented accuracy in identifying where institutional money is likely to react to price action.
🚀Points of Innovation
● CNN-Inspired Pivot Analysis - Advanced binning system using convolutional neural network principles for superior pattern recognition
● Real-Time Probability Engine - Live reaction probability calculations using 9-factor logistic regression model
● Dynamic Zone Intelligence - Automatic zone merging using Intersection over Union (IoU) algorithms
● Volume-Weighted Scoring - Time-of-day volume Z-score analysis for enhanced zone strength assessment
● Adaptive Decay System - Intelligent zone lifecycle management based on touch frequency and recency
● Multi-Filter Architecture - Optional gradient, smoothing, and Difference of Gaussians (DoG) convolution filters
🔧Core Components
● Pivot Detection Engine - Advanced pivot identification with configurable left/right bars and ATR-normalized strength calculations
● Neural Network Binning - Price level clustering using CNN-inspired algorithms with ATR-based bin sizing
● Logistic Regression Model - 9-factor probability calculation including distance, width, volume, VWAP deviation, and trend analysis
● Zone Management System - Intelligent creation, merging, and decay algorithms for optimal zone lifecycle control
● Visualization Layer - Dynamic line drawing with opacity-based scoring and optional zone fills
🔥Key Features
● High-Probability Zone Detection - Automatically identifies institutional levels with reaction probabilities above configurable thresholds
● Real-Time Probability Scoring - Live calculation of zone reaction likelihood using advanced statistical modeling
● Session-Aware Analysis - Optional filtering to specific trading sessions for enhanced accuracy during active market hours
● Customizable Parameters - Full control over lookback periods, zone sensitivity, merge thresholds, and probability models
● Performance Optimized - Efficient processing with controlled update frequencies and pivot processing limits
● Non-Repainting Mode - Strict mode available for backtesting accuracy and live trading reliability
🎨Visualization
● Dynamic Zone Lines - Color-coded support and resistance levels with opacity reflecting zone strength and confidence scores
● Probability Labels - Real-time display of reaction probabilities, touch counts, and historical hit rates for active zones
● Zone Fills - Optional semi-transparent zone highlighting for enhanced visual clarity and immediate pattern recognition
● Adaptive Styling - Automatic color and opacity adjustments based on zone scoring and statistical significance
📖Usage Guidelines
● Lookback Bars - Default 500, Range 100-1000, Controls the historical data window for pivot analysis and zone calculation
● Pivot Left/Right - Default 3, Range 1-10, Defines the pivot detection sensitivity and confirmation requirements
● Bin Size ATR units - Default 0.25, Range 0.1-2.0, Controls price level clustering granularity for zone creation
● Base Zone Half-Width ATR units - Default 0.25, Range 0.1-1.0, Sets the minimum zone width in ATR units for institutional level boundaries
● Zone Merge IoU Threshold - Default 0.5, Range 0.1-0.9, Intersection over Union threshold for automatic zone merging algorithms
● Max Active Zones - Default 5, Range 3-20, Maximum number of zones displayed simultaneously to prevent chart clutter
● Probability Threshold for Labels - Default 0.6, Range 0.3-0.9, Minimum reaction probability required for zone label display and alerts
● Distance Weight w1 - Controls influence of price distance from zone center on reaction probability
● Width Weight w2 - Adjusts impact of zone width on probability calculations
● Volume Weight w3 - Modifies volume Z-score influence on zone strength assessment
● VWAP Weight w4 - Controls VWAP deviation impact on institutional level significance
● Touch Count Weight w5 - Adjusts influence of historical zone interactions on probability scoring
● Hit Rate Weight w6 - Controls prior success rate impact on future reaction likelihood predictions
● Wick Penetration Weight w7 - Modifies wick penetration analysis influence on probability calculations
● Trend Weight w8 - Adjusts trend context impact using ADX analysis for directional bias assessment
✅Best Use Cases
● Swing Trading Entries - Enter positions at high-probability institutional zones with 60%+ reaction scores
● Scalping Opportunities - Quick entries and exits around frequently tested institutional levels
● Risk Management - Use zones as dynamic stop-loss and take-profit levels based on institutional behavior
● Market Structure Analysis - Identify key institutional levels that define current market structure and sentiment
● Confluence Trading - Combine with other technical indicators for high-probability trade setups
● Session-Based Strategies - Focus analysis during high-volume sessions for maximum effectiveness
⚠️Limitations
● Historical Pattern Dependency - Algorithm effectiveness relies on historical patterns that may not repeat in changing market conditions
● Computational Intensity - Complex calculations may impact chart performance on lower-end devices or with multiple indicators
● Probability Estimates - Reaction probabilities are statistical estimates and do not guarantee actual market outcomes
● Session Sensitivity - Performance may vary significantly between different market sessions and volatility regimes
● Parameter Sensitivity - Results can be highly dependent on input parameters requiring optimization for different instruments
💡What Makes This Unique
● CNN Architecture - First indicator to apply convolutional neural network principles to institutional-level detection
● Real-Time ML Scoring - Live machine learning probability calculations for each zone interaction
● Advanced Zone Management - Sophisticated algorithms for zone lifecycle management and automatic optimization
● Statistical Rigor - Comprehensive 9-factor logistic regression model with extensive backtesting validation
● Performance Optimization - Efficient processing algorithms designed for real-time trading applications
🔬How It Works
● Multi-timeframe pivot identification - Uses configurable sensitivity parameters for advanced pivot detection
● ATR-normalized strength calculations - Standardizes pivot significance across different volatility regimes
● Volume Z-score integration - Enhanced pivot weighting based on time-of-day volume patterns
● Price level clustering - Neural network binning algorithms with ATR-based sizing for zone creation
● Recency decay applications - Weights recent pivots more heavily than historical data for relevance
● Statistical filtering - Eliminates low-significance price levels and reduces market noise
● Dynamic zone generation - Creates zones from statistically significant pivot clusters with minimum support thresholds
● IoU-based merging algorithms - Combines overlapping zones while maintaining accuracy using Intersection over Union
● Adaptive decay systems - Automatic removal of outdated or low-performing zones for optimal performance
● 9-factor logistic regression - Incorporates distance, width, volume, VWAP, touch history, and trend analysis
● Real-time scoring updates - Zone interaction calculations with configurable threshold filtering
● Optional CNN filters - Gradient detection, smoothing, and Difference of Gaussians processing for enhanced accuracy
💡Note
This indicator represents advanced quantitative analysis and should be used by traders familiar with statistical modeling concepts. The probability scores are mathematical estimates based on historical patterns and should be combined with proper risk management and additional technical analysis for optimal trading decisions. Indicator
Mean Reversion Probability Zones [BigBeluga]🔵 OVERVIEW
The Mean Reversion Probability Zones indicator measures the likelihood of price reverting back toward its mean . By analyzing oscillator dynamics (RSI, MFI, or Stochastic), it calculates probability zones both above and below the oscillator. These zones are visualized as histograms, colored regions on the main chart, and a compact dashboard, helping traders spot when the market is statistically stretched and more likely to revert.
🔵 CONCEPTS
Mean Reversion : The tendency of price to return to its average after significant extensions.
Oscillator-Based Analysis : Uses RSI, MFI, or Stochastic as the base signal for detecting overextension.
Probability Model : The probability of reversion is computed using three factors:
Whether the oscillator is rising or declining.
Whether the oscillator is above or below user-defined thresholds.
The oscillator’s actual value (distance from equilibrium).
Dual-Zone Output :
Upper histogram = probability of downward mean reversion.
Lower histogram = probability of upward mean reversion.
Historical Extremes : The dashboard highlights the recent maximum probability values for both upward and downward scenarios.
🔵 FEATURES
Oscillator Choice : Switch between RSI, MFI, and Stochastic.
Customizable Zones : User-defined upper/lower thresholds with independent colors.
Probability Histograms :
Above oscillator → down reversion probability.
Below oscillator → up reversion probability.
Colored Gradient Zones on Chart : Visual overlays showing where mean reversion probabilities are strongest.
Probability Labels : Percentages displayed next to histogram values for clarity.
Dashboard : Compact table in the corner showing the recent maximum probabilities for both upward and downward mean reversion.
Overlay Compatibility : Works in both chart pane and sub-pane with oscillators.
🔵 HOW TO USE
Set Oscillator : Choose RSI, MFI, or Stochastic depending on your strategy style.
Adjust Zones : Define upper/lower bounds for when oscillator values indicate strong overbought/oversold conditions.
Interpret Histograms :
Orange (upper) histogram → higher chance of a pullback/downward mean reversion.
Green (lower) histogram → higher chance of upward reversion/bounce.
Watch Gradient Zones : On the main chart, shaded areas highlight where probability of mean reversion is elevated.
Consult Dashboard : Use the “Recent MAX” values to understand how strong recent reversion probabilities have been in either direction.
Confluence Strategy : Combine with support/resistance, order flow, or trend filters to avoid counter-trend trades.
🔵 CONCLUSION
The Mean Reversion Probability Zones provides traders with an advanced way to quantify and visualize mean reversion opportunities. By blending oscillator momentum, threshold logic, and probability calculations, it highlights when markets are statistically stretched and primed for reversal. Whether you are a contrarian trader or simply looking for exhaustion signals to fade, this tool helps bring structure and clarity to mean reversion setups. Indicator
BUY & SELL Probability (M5..D1) - MTFMTF Probability Indicator (M5 to D1)
Indicator — Dual Histogram with Buy/Sell Labels
This indicator is designed to provide a probabilistic bias for bullish or bearish conditions by combining three different analytical components across multiple timeframes. The goal is to reduce noise from single-indicator signals and instead highlight confluence where trend, momentum, and strength agree.
Why this combination is useful
- EMA(200) Trend Filter: Identifies whether price is trading above or below a widely used long-term moving average.
- MACD Momentum: Detects short-term directional momentum through line crossovers.
- ADX Strength: Measures how strong the trend is, preventing signals in weak or flat markets.
By combining these, the indicator avoids situations where one tool signals a trade but others do not, helping to filter out low-probability setups.
How it works
- Each timeframe (M5, M15, H1, H4, D1) generates its own trend, momentum, and strength score.
- Scores are weighted according to user-defined importance and then aggregated into a single probability.
- Proximity to recent support and resistance levels can adjust the final score, accounting for nearby barriers.
- The final probability is displayed as:
- Histogram (subwindow): Green bars for bullish probability >50%, red bars for bearish <50%.
- On-chart labels: Showing exact buy/sell percentages on the last bar for quick reference.
Inputs
- EMA length (default 200), MACD settings, ADX period.
- Weights for each timeframe and component (trend, momentum, strength).
- Optional boost for the chart’s current timeframe.
- Smoothing length for probability values.
- Lookback period for support/resistance adjustment.
How to use it
- A green histogram above zero indicates bullish probability >50%.
- A red histogram below zero indicates bearish probability >50%.
- Neutral readings near 50% show low confluence and may be best avoided.
- Users can adjust weights to emphasize higher or lower timeframes, depending on their trading style.
Notes
- This script does not guarantee profitable trades.
- Best used together with price action, volume, or additional confirmation tools.
- Signals are calculated only on closed bars to avoid repainting.
- For testing and learning purposes — not financial advice. Indicator
Stop Loss vs Take Profit Probability and EVThis stop loss and take profit calculator uses a Monte Carlo simulation to calculate the probability of hitting your Stop Loss or Take Profit levels across different time horizons (expressed in bars).
It provides data-driven insights to optimize your risk management and position sizing by showing Expected Value for each scenario.
As a quant, I love using statistical data to help my decisions and get better EV from my trades.
🔬 How It's Calculated
Monte Carlo Simulation: Runs 1,000-10,000 price simulations using a random walk model
Volatility Analysis: Combines ATR-based and Historical Volatility for accurate price movement modeling
Expected Value: Calculates profit/loss expectation using formula: (TP_Probability × Reward) - (SL_Probability × Risk)
Time Horizons: Tests multiple timeframes (1, 5, 10, 20, 50 bars) to find optimal holding periods
Risk/Reward Ratios: Automatically calculates and displays R:R ratios for quick assessment
💡 Use Cases
Position Sizing - Determine optimal risk per trade based on Expected Value
Time Horizon Optimization - Find the best holding period for your strategy
Stop Loss Placement - Validate SL levels using probability analysis
Take Profit Optimization - Set TP levels with statistical backing
Strategy Backtesting - Compare different R:R setups before entering trades
Risk Management - Avoid trades with negative Expected Value
Swing vs Day Trading - Choose timeframes with highest success probability
🎯 How to Use
Setup Trade: Enter your entry price, stop loss, and take profit levels
You can add or remove time horizons denominated in bars. Say you are looking at 1h candles, adding a 24-bar time horizon means you are looking into 24 hours
Choose Direction: Select Long or Short position
Review Table
Analyze Expected Value: Focus on positive EV scenarios (green background)
Optimize Timing: Select time horizons with best risk/reward profile
Adjust Parameters: Modify volatility calculation method and simulation count if needed
Examples
Here's how you can read the tables.
Example 1:
In this chart, we are analyzing the TP and SL probabilities as well as the EV (expected value) for a stock. I want to check what the likelihood is that my SL and TP get triggered over the next 5 days. The stock market is open for 6.5 hours per day, which is 13 bars in this 30-minute bar chart. 26 bars is 2 days, 39 bars is 3 days and so on.
Although this trade is more likely to trigger my SL than my TP, in some of the time horizons we have a positive expected value because of the risk/reward of our trade (i.e. distance of the SL and TP from the price) and the probability of hitting SL and TP.
Example 2:
In this example, we have applied the indicator to gold. Because the TP is much closer to the price, the probability of hitting the TP is much higher.
We can also observe that the expected Value in the shorter time frames is better than in the longer ones. This can give us some clues to set up our trade. If we know that the EV is positive, we can allocate more to that specific trade.
Enjoy, and please let me know your feedback! 😊🥂 Indicator
Advanced Range Analyzer ProAdvanced Range Analyzer Pro – Adaptive Range Detection & Breakout Forecasting
Overview
Advanced Range Analyzer Pro is a comprehensive trading tool designed to help traders identify consolidations, evaluate their strength, and forecast potential breakout direction. By combining volatility-adjusted thresholds, volume distribution analysis, and historical breakout behavior, the indicator builds an adaptive framework for navigating sideways price action. Instead of treating ranges as noise, this system transforms them into opportunities for mean reversion or breakout trading.
How It Works
The indicator continuously scans price action to identify active range environments. Ranges are defined by volatility compression, repeated boundary interactions, and clustering of volume near equilibrium. Once detected, the indicator assigns a strength score (0–100), which quantifies how well-defined and compressed the consolidation is.
Breakout probabilities are then calculated by factoring in:
Relative time spent near the upper vs. lower range boundaries
Historical breakout tendencies for similar structures
Volume distribution inside the range
Momentum alignment using auxiliary filters (RSI/MACD)
This creates a live probability forecast that updates as price evolves. The tool also supports range memory, allowing traders to analyze the last completed range after a breakout has occurred. A dynamic strength meter is displayed directly above each consolidation range, providing real-time insight into range compression and breakout potential.
Signals and Breakouts
Advanced Range Analyzer Pro includes a structured set of visual tools to highlight actionable conditions:
Range Zones – Gradient-filled boxes highlight active consolidations.
Strength Meter – A live score displayed in the dashboard quantifies compression.
Breakout Labels – Probability percentages show bias toward bullish or bearish continuation.
Breakout Highlights – When a breakout occurs, the range is marked with directional confirmation.
Dashboard Table – Displays current status, strength, live/last range mode, and probabilities.
These elements update in real time, ensuring that traders always see the current state of consolidation and breakout risk.
Interpretation
Range Strength : High scores (70–100) indicate strong consolidations likely to resolve explosively, while low scores suggest weak or choppy ranges prone to false signals.
Breakout Probability : Directional bias greater than 60% suggests meaningful breakout pressure. Equal probabilities indicate balanced compression, favoring mean-reversion strategies.
Market Context : Ranges aligned with higher timeframe trends often resolve in the dominant direction, while counter-trend ranges may lead to reversals or liquidity sweeps.
Volatility Insight : Tight ranges with low ATR imply imminent expansion; wide ranges signal extended consolidation or distribution phases.
Strategy Integration
Advanced Range Analyzer Pro can be applied across multiple trading styles:
Breakout Trading : Enter on probability shifts above 60% with confirmation of volume or momentum.
Mean Reversion : Trade inside ranges with high strength scores by fading boundaries and targeting equilibrium.
Trend Continuation : Focus on ranges that form mid-trend, anticipating continuation after consolidation.
Liquidity Sweeps : Use failed breakouts at boundaries to capture reversals.
Multi-Timeframe : Apply on higher timeframes to frame market context, then execute on lower timeframes.
Advanced Techniques
Combine with volume profiles to identify areas of institutional positioning within ranges.
Track sequences of strong consolidations for trend development or exhaustion signals.
Use breakout probability shifts in conjunction with order flow or momentum indicators to refine entries.
Monitor expanding/contracting range widths to anticipate volatility cycles.
Custom parameters allow fine-tuning sensitivity for different assets (crypto, forex, equities) and trading styles (scalping, intraday, swing).
Inputs and Customization
Range Detection Sensitivity : Controls how strictly ranges are defined.
Strength Score Settings : Adjust weighting of compression, volume, and breakout memory.
Probability Forecasting : Enable/disable directional bias and thresholds.
Gradient & Fill Options : Customize range visualization colors and opacity.
Dashboard Display : Toggle live vs last range, info table size, and position.
Breakout Highlighting : Choose border/zone emphasis on breakout events.
Why Use Advanced Range Analyzer Pro
This indicator provides a data-driven approach to trading consolidation phases, one of the most common yet underutilized market states. By quantifying range strength, mapping probability forecasts, and visually presenting risk zones, it transforms uncertainty into clarity.
Whether you’re trading breakouts, fading ranges, or mapping higher timeframe context, Advanced Range Analyzer Pro delivers a structured, adaptive framework that integrates seamlessly into multiple strategies.
Indicator
Seasonality Monte Carlo Forecaster [BackQuant]Seasonality Monte Carlo Forecaster
Plain-English overview
This tool projects a cone of plausible future prices by combining two ideas that traders already use intuitively: seasonality and uncertainty. It watches how your market typically behaves around this calendar date, turns that seasonal tendency into a small daily “drift,” then runs many randomized price paths forward to estimate where price could land tomorrow, next week, or a month from now. The result is a probability cone with a clear expected path, plus optional overlays that show how past years tended to move from this point on the calendar. It is a planning tool, not a crystal ball: the goal is to quantify ranges and odds so you can size, place stops, set targets, and time entries with more realism.
What Monte Carlo is and why quants rely on it
• Definition . Monte Carlo simulation is a way to answer “what might happen next?” when there is randomness in the system. Instead of producing a single forecast, it generates thousands of alternate futures by repeatedly sampling random shocks and adding them to a model of how prices evolve.
• Why it is used . Markets are noisy. A single point forecast hides risk. Monte Carlo gives a distribution of outcomes so you can reason in probabilities: the median path, the 68% band, the 95% band, tail risks, and the chance of hitting a specific level within a horizon.
• Core strengths in quant finance .
– Path-dependent questions : “What is the probability we touch a stop before a target?” “What is the expected drawdown on the way to my objective?”
– Pricing and risk : Useful for path-dependent options, Value-at-Risk (VaR), expected shortfall (CVaR), stress paths, and scenario analysis when closed-form formulas are unrealistic.
– Planning under uncertainty : Portfolio construction and rebalancing rules can be tested against a cloud of plausible futures rather than a single guess.
• Why it fits trading workflows . It turns gut feel like “seasonality is supportive here” into quantitative ranges: “median path suggests +X% with a 68% band of ±Y%; stop at Z has only ~16% odds of being tagged in N days.”
How this indicator builds its probability cone
1) Seasonal pattern discovery
The script builds two day-of-year maps as new data arrives:
• A return map where each calendar day stores an exponentially smoothed average of that day’s log return (yesterday→today). The smoothing (90% old, 10% new) behaves like an EWMA, letting older seasons matter while adapting to new information.
• A volatility map that tracks the typical absolute return for the same calendar day.
It calculates the day-of-year carefully (with leap-year adjustment) and indexes into a 365-slot seasonal array so “March 18” is compared with past March 18ths. This becomes the seasonal bias that gently nudges simulations up or down on each forecast day.
2) Choice of randomness engine
You can pick how the future shocks are generated:
• Daily mode uses a Gaussian draw with the seasonal bias as the mean and a volatility that comes from realized returns, scaled down to avoid over-fitting. It relies on the Box–Muller transform internally to turn two uniform random numbers into one normal shock.
• Weekly mode uses bootstrap sampling from the seasonal return history (resampling actual historical daily drifts and then blending in a fraction of the seasonal bias). Bootstrapping is robust when the empirical distribution has asymmetry or fatter tails than a normal distribution.
Both modes seed their random draws deterministically per path and day, which makes plots reproducible bar-to-bar and avoids flickering bands.
3) Volatility scaling to current conditions
Markets do not always live in average volatility. The engine computes a simple volatility factor from ATR(20)/price and scales the simulated shocks up or down within sensible bounds (clamped between 0.5× and 2.0×). When the current regime is quiet, the cone narrows; when ranges expand, the cone widens. This prevents the classic mistake of projecting calm markets into a storm or vice versa.
4) Many futures, summarized by percentiles
The model generates a matrix of price paths (capped at 100 runs for performance inside PulseWire), each path stepping forward for your selected horizon. For each forecast day it sorts the simulated prices and pulls key percentiles:
• 5th and 95th → approximate 95% band (outer cone).
• 16th and 84th → approximate 68% band (inner cone).
• 50th → the median or “expected path.”
These are drawn as polylines so you can immediately see central tendency and dispersion.
5) A historical overlay (optional)
Turn on the overlay to sketch a dotted path of what a purely seasonal projection would look like for the next ~30 days using only the return map, no randomness. This is not a forecast; it is a visual reminder of the seasonal drift you are biasing toward.
Inputs you control and how to think about them
Monte Carlo Simulation
• Price Series for Calculation . The source series, typically close.
• Enable Probability Forecasts . Master switch for simulation and drawing.
• Simulation Iterations . Requested number of paths to run. Internally capped at 100 to protect performance, which is generally enough to estimate the percentiles for a trading chart. If you need ultra-smooth bands, shorten the horizon.
• Forecast Days Ahead . The length of the cone. Longer horizons dilute seasonal signal and widen uncertainty.
• Probability Bands . Draw all bands, just 95%, just 68%, or a custom level (display logic remains 68/95 internally; the custom number is for labeling and color choice).
• Pattern Resolution . Daily leans on day-of-year effects like “turn-of-month” or holiday patterns. Weekly biases toward day-of-week tendencies and bootstraps from history.
• Volatility Scaling . On by default so the cone respects today’s range context.
Plotting & UI
• Probability Cone . Plots the outer and inner percentile envelopes.
• Expected Path . Plots the median line through the cone.
• Historical Overlay . Dotted seasonal-only projection for context.
• Band Transparency/Colors . Customize primary (outer) and secondary (inner) band colors and the mean path color. Use higher transparency for cleaner charts.
What appears on your chart
• A cone starting at the most recent bar, fanning outward. The outer lines are the ~95% band; the inner lines are the ~68% band.
• A median path (default blue) running through the center of the cone.
• An info panel on the final historical bar that summarizes simulation count, forecast days, number of seasonal patterns learned, the current day-of-year, expected percentage return to the median, and the approximate 95% half-range in percent.
• Optional historical seasonal path drawn as dotted segments for the next 30 bars.
How to use it in trading
1) Position sizing and stop logic
The cone translates “volatility plus seasonality” into distances.
• Put stops outside the inner band if you want only ~16% odds of a stop-out due to noise before your thesis can play.
• Size positions so that a test of the inner band is survivable and a test of the outer band is rare but acceptable.
• If your target sits inside the 68% band at your horizon, the payoff is likely modest; outside the 68% but inside the 95% can justify “one-good-push” trades; beyond the 95% band is a low-probability flyer—consider scaling plans or optionality.
2) Entry timing with seasonal bias
When the median path slopes up from this calendar date and the cone is relatively narrow, a pullback toward the lower inner band can be a high-quality entry with a tight invalidation. If the median slopes down, fade rallies toward the upper band or step aside if it clashes with your system.
3) Target selection
Project your time horizon to N bars ahead, then pick targets around the median or the opposite inner band depending on your style. You can also anchor dynamic take-profits to the moving median as new bars arrive.
4) Scenario planning & “what-ifs”
Before events, glance at the cone: if the 95% band already spans a huge range, trade smaller, expect whips, and avoid placing stops at obvious band edges. If the cone is unusually tight, consider breakout tactics and be ready to add if volatility expands beyond the inner band with follow-through.
5) Options and vol tactics
• When the cone is tight : Prefer long gamma structures (debit spreads) only if you expect a regime shift; otherwise premium selling may dominate.
• When the cone is wide : Debit structures benefit from range; credit spreads need wider wings or smaller size. Align with your separate IV metrics.
Reading the probability cone like a pro
• Cone slope = seasonal drift. Upward slope means the calendar has historically favored positive drift from this date, downward slope the opposite.
• Cone width = regime volatility. A widening fan tells you that uncertainty grows fast; a narrow cone says the market typically stays contained.
• Mean vs. price gap . If spot trades well above the median path and the upper band, mean-reversion risk is high. If spot presses the lower inner band in an up-sloping cone, you are in the “buy fear” zone.
• Touches and pierces . Touching the inner band is common noise; piercing it with momentum signals potential regime change; the outer band should be rare and often brings snap-backs unless there is a structural catalyst.
Methodological notes (what the code actually does)
• Log returns are used for additivity and better statistical behavior: sim_ret is applied via exp(sim_ret) to evolve price.
• Seasonal arrays are updated online with EWMA (90/10) so the model keeps learning as each bar arrives.
• Leap years are handled; indexing still normalizes into a 365-slot map so the seasonal pattern remains stable.
• Gaussian engine (Daily mode) centers shocks on the seasonal bias with a conservative standard deviation.
• Bootstrap engine (Weekly mode) resamples from observed seasonal returns and adds a fraction of the bias, which captures skew and fat tails better.
• Volatility adjustment multiplies each daily shock by a factor derived from ATR(20)/price, clamped between 0.5 and 2.0 to avoid extreme cones.
• Performance guardrails : simulations are capped at 100 paths; the probability cone uses polylines (no heavy fills) and only draws on the last confirmed bar to keep charts responsive.
• Prerequisite data : at least ~30 seasonal entries are required before the model will draw a cone; otherwise it waits for more history.
Strengths and limitations
• Strengths :
– Probabilistic thinking replaces single-point guessing.
– Seasonality adds a small but meaningful directional bias that many markets exhibit.
– Volatility scaling adapts to the current regime so the cone stays realistic.
• Limitations :
– Seasonality can break around structural changes, policy shifts, or one-off events.
– The number of paths is performance-limited; percentile estimates are good for trading, not for academic precision.
– The model assumes tomorrow’s randomness resembles recent randomness; if regime shifts violently, the cone will lag until the EWMA adapts.
– Holidays and missing sessions can thin the seasonal sample for some assets; be cautious with very short histories.
Tuning guide
• Horizon : 10–20 bars for tactical trades; 30+ for swing planning when you care more about broad ranges than precise targets.
• Iterations : The default 100 is enough for stable 5/16/50/84/95 percentiles. If you crave smoother lines, shorten the horizon or run on higher timeframes.
• Daily vs. Weekly : Daily for equities and crypto where month-end and turn-of-month effects matter; Weekly for futures and FX where day-of-week behavior is strong.
• Volatility scaling : Keep it on. Turn off only when you intentionally want a “pure seasonality” cone unaffected by current turbulence.
Workflow examples
• Swing continuation : Cone slopes up, price pulls into the lower inner band, your system fires. Enter near the band, stop just outside the outer line for the next 3–5 bars, target near the median or the opposite inner band.
• Fade extremes : Cone is flat or down, price gaps to the upper outer band on news, then stalls. Favor mean-reversion toward the median, size small if volatility scaling is elevated.
• Event play : Before CPI or earnings on a proxy index, check cone width. If the inner band is already wide, cut size or prefer options structures that benefit from range.
Good habits
• Pair the cone with your entry engine (breakout, pullback, order flow). Let Monte Carlo do range math; let your system do signal quality.
• Do not anchor blindly to the median; recalc after each bar. When the cone’s slope flips or width jumps, the plan should adapt.
• Validate seasonality for your symbol and timeframe; not every market has strong calendar effects.
Summary
The Seasonality Monte Carlo Forecaster wraps institutional risk planning into a single overlay: a data-driven seasonal drift, realistic volatility scaling, and a probabilistic cone that answers “where could we be, with what odds?” within your trading horizon. Use it to place stops where randomness is less likely to take you out, to set targets aligned with realistic travel, and to size positions with confidence born from distributions rather than hunches. It will not predict the future, but it will keep your decisions anchored to probabilities—the language markets actually speak. Indicator
