[GYTS-CE] Kinetic Trend Envelope (adaptive trailing stop)Kinetic Trend Envelope (Community Edition)
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What is the Kinetic Trend Envelope?
The Kinetic Trend Envelope (KTE) is an adaptive directional trailing stop in the lineage of SuperTrend, rebuilt around the premise that volatility is kinetic energy . It measures per-bar motion with five academically grounded volatility estimators, then widens the envelope as energy rises and contracts it as motion settles.
In an uptrend, the lower band ratchets higher and never retreats; in a downtrend, the upper band ratchets lower. The direction changes when the active stop is breached, after which the opposite side becomes the new trailing stop.
💮 Why Use This Indicator?
Conventional trailing stops typically combine a price anchor with one symmetric ATR-derived width. The KTE extends that model with:
Asymmetric volatility profiling — Bullish- and bearish-candle volatility shape the upper and lower bands independently.
Three direction-switch methods — High/low, close, or a smoothed estimator controls flip sensitivity without moving the band anchor.
Five volatility estimators — ATR plus Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang covers different treatments of gaps, drift, and intrabar range.
The outputs are calibrated to a common width basis, so Volatility Factor remains interpretable across estimators and price scales. Fine adjustment may still be useful, but switching estimators should not require re-tuning by orders of magnitude.
↑ The KTE on a trending instrument. The thick line is the active trailing stop; the thin line shows the opposing side of the envelope. Both expand and contract with market energy.
↑ KTE beside PulseWire's built-in SuperTrend, both using ATR with a 10-bar lookback. KTE's asymmetric profile changes how each side responds to directional volatility while the monotonic active band avoids premature loosening.
🌸 --------- HOW IT WORKS --------- 🌸
💮 Core Concept
The bands share a smoothed price estimator as their anchor, but use separate volatility profiles:
Upper band = estimator + (factor × bullish-candle volatility)
Lower band = estimator − (factor × bearish-candle volatility)
In a bullish state, the lower band is active and can only rise. In a bearish state, the upper band is active and can only fall. This monotonic constraint prevents a live trailing stop from loosening within the trend.
The selected direction-switch method changes only the breach test. It does not change the smoothed estimator anchoring the envelope, so a wick-sensitive trigger cannot drag the bands around with the wick.
💮 The Five Volatility Estimators
Each estimator reads a different part of the OHLC bar:
ATR (Wilder, 1978) — Familiar baseline that handles gaps through true range.
Parkinson (1980) — Uses high-low range; efficient under continuous, low-drift conditions.
Garman-Klass (1980) — Adds open-close information; favours continuous sessions without material gaps.
Rogers-Satchell (1991) — Drift-independent and well suited to trending, continuously traded instruments.
Yang-Zhang (2000) — Combines overnight gaps, open-close movement, and Rogers-Satchell; the gap-aware default.
Statistical efficiency does not guarantee a visibly tighter stop. At slow Adaptation Speed settings, long averaging makes the estimators look similar; at fast settings, their different treatments of gaps, drift, and range become more visible. Choose according to the instrument's behaviour rather than expecting one estimator always to produce the narrowest band.
↑ ATR and Yang-Zhang at Adaptation Speed 2. The long profile memory (low speed) smooths away most of the difference, so the two envelopes nearly overlap.
↑ ATR and Yang-Zhang at Adaptation Speed 8. The short profile memory (high speed) exposes their different volatility readings, producing visibly distinct envelope widths.
💮 Asymmetric Volatility Profiling and Adaptation Speed
The KTE stores volatility from bullish and bearish candles separately. Bullish samples determine the upper width; bearish samples determine the lower width. This allows the two sides to respond differently when upward and downward motion carry different energy.
Adaptation Speed controls the memory of this profile, not the speed of the price estimator and not the distance of the stop by itself. Its 1–10 scale maps logarithmically to an internal window:
Speed 3 — approximately 878 bars: stable and slow to re-weight
Default 3.5 — approximately 570 bars: general-purpose smoothing
Speed 8 — approximately 11 bars: highly responsive to recent volatility
Speed 10 — approximately 2 bars: extremely reactive and noisy
Faster does not necessarily mean closer to price. During a volatility burst, a fast profile recognises the expansion sooner and may widen the band sharply. Because the active stop cannot loosen, it can then remain flat until the estimator catches up. A slow profile dilutes the same burst across much more history, so its narrower band may appear to follow price faster.
This is why two instances matched during a calm period can separate during a shock, especially when they also use different Volatility Factor values. Compare Adaptation Speed with the same factor first; matching lines in one regime does not make two configurations equivalent elsewhere.
The profiles are also direction-conditioned: bullish samples are replaced by later bullish candles and bearish samples by later bearish candles. A recent high-volatility sample can therefore persist through a run of opposite-colour candles, producing deliberate step-like plateaux in the relevant band.
↑ Asymmetric profiling in action: the upper and lower widths respond independently to bullish- and bearish-candle volatility.
💮 Direction Switch Methods
The breach source sets the balance between responsiveness and false flips:
On high/low — Uses the current bar's wick and can switch on the breach bar. Fastest and most sensitive to noise.
On close — Uses the previous confirmed close; the switch appears on the following bar.
On estimator — Uses the previous smoothed estimator; the most conservative default, also switching on the following bar.
↑ The three switch methods share the same band geometry but change direction at different times.
🌸 --------- KEY FEATURES --------- 🌸
💮 Eight Estimator Filters
The configurable price anchor includes:
Ultimate Smoother, 2- or 3-pole — Low-noise, near-zero-lag passband response; the 2-pole version is the default.
Super Smoother, 2- or 3-pole — Ehlers low-pass filters for progressively stronger smoothing.
BiQuad — Second-order low-pass filter with an adjustable Q-factor.
ADXvma — Adapts to trend strength and tends to flatten in ranges.
MAMA — Cycle-adaptive MESA moving average.
A2RMA — Adaptive recursive moving average with adjustable gamma.
They are provided by the open-source FiltersToolkit library.
💮 Visual Layering
The display separates function from context:
Active band — Thick directional trailing-stop line
Opposing band — Thin reference for the inactive side
Channel fill — Visual separation between the estimator and each band
Estimator — Optional smoothed anchor
Palette, light/dark mode, widths, and transparencies can be adjusted independently.
🌸 --------- USAGE GUIDE --------- 🌸
💮 Getting Started
Start with the defaults, observe several calm and volatile regimes, and change one dimension at a time:
Tune Volatility Factor for the preferred stop distance.
Tune Adaptation Speed for how quickly width should respond to regime changes.
Choose the direction-switch method for the preferred confirmation level.
Change the volatility estimator only when its assumptions better fit the instrument.
💮 Choosing a Volatility Estimator
Gapped equities — Yang-Zhang accounts for overnight movement.
Trending 24/7 markets — Rogers-Satchell is drift-independent without a separate gap component.
Continuous, range-led markets — Parkinson or Garman-Klass offers efficient range-based measurement under their assumptions.
Familiar baseline — ATR provides conventional true-range behaviour.
On continuous instruments, Rogers-Satchell and Yang-Zhang may look very similar because there are few gaps to distinguish them. Use the Volatility Toolkit to compare their raw behaviour on the intended instrument.
↑ Three estimators compared on one instrument, each reading a different combination of OHLC information.
💮 Tuning Width and Responsiveness
These controls solve different problems:
Volatility Factor — Sets the distance per unit of measured volatility.
Adaptation Speed — Sets the memory of the bullish/bearish profile; faster can widen the stop sooner during shocks.
Volatility Lookback — Sets how quickly the underlying per-bar volatility estimate changes.
Estimator Lookback — Sets the smoothness of the price anchor.
Use symptoms to guide adjustment:
Frequent flips on minor pullbacks — Increase Volatility Factor or use a more conservative switch method (e.g. "on estimator").
Excessive give-back — Decrease Volatility Factor or use a more responsive switch method (e.g. "on high/low").
Width reacts too slowly to regime changes — Increase Adaptation Speed or reduce Volatility Lookback.
Bands become erratic during shocks — Reduce Adaptation Speed or increase Volatility Lookback.
↑ A tight factor follows price more closely and flips more often; a loose factor tolerates larger pullbacks.
💮 Trading Applications
Discretionary trailing stop — Move a protective stop with the active band as it tightens.
Trend confirmation — Accept long signals only during a bullish KTE state, and short signals only while bearish.
Exit timing — Treat a direction change as an exit when the trade thesis is trend-following.
💮 Integration with GYTS Suite
The visible bands and estimator can be selected as sources by compatible Pine scripts. Two packed streams are also exposed:
🔗 STREAM KTE 🪜 Trailing Stoploss — Positive lower-band value in a bullish state; negative upper-band value in a bearish state.
🔗 STREAM KTE 🪜 Mechanism — Encodes the switch method and scale-invariant estimator relationship for compatible consumers.
The KTE is, first and foremost, a trailing stop, and these streams are built for stop management. The Order Orchestrator strategy consumes the Trailing Stoploss and Mechanism streams together : the first supplies the active stop level and its direction, the second makes the strategy's trailing-exit runner follow whatever switch method and estimator you set here. So the stop is configured once, in the KTE.
Beyond that primary role, the signed trailing-stop stream can also serve as a trend signal, since its sign flips with direction: it can be read through sign and magnitude as an entry/exit signal, including by Flux Composer . The KTE can also be paired with Market Regime Detector so flips are acted on only when the broader regime supports trend-following behaviour.
🌸 --------- LIMITATIONS --------- 🌸
Trailing-stop latency — Every trailing stop gives back some of the move between the trend extreme and the eventual breach.
Whipsaws in ranges — Low-energy chop can produce repeated flips; a regime filter may help when ranging conditions dominate.
Fast adaptation can widen the stop — Higher Adaptation Speed means faster volatility response, not guaranteed proximity to price.
Direction-conditioned memory — A bullish or bearish outlier remains in its own profile until enough matching-direction samples replace it, which can create plateaux after shocks.
Warm-up and sample size — Long profile windows need sufficient chart history; strongly one-sided markets may leave one side with few recent samples.
🌸 --------- CREDITS --------- 🌸
💮 Academic Sources
Wilder, J. W. (1978). New Concepts in Technical Trading Systems . Trend Research.
Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53 (1), 61–65. DOI
Garman, M. B., & Klass, M. J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53 (1), 67–78. DOI
Rogers, L. C. G., & Satchell, S. E. (1991). Estimating Variance from High, Low and Closing Prices. Annals of Applied Probability, 1 (4), 504–512. DOI
Yang, D., & Zhang, Q. (2000). Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices. Journal of Business, 73 (3), 477–491. DOI
Ehlers, J. F. (2024). The Ultimate Smoother. Technical Analysis of Stocks & Commodities , 2024-04. TASC
Ehlers, J. F. (2004). Cybernetic Analysis for Stocks and Futures . Wiley. Covers SuperSmoother, MAMA and more.
💮 Inspiration
Thanks to Trendoscope for inspiring us with the Supertrend - Ladder ATR (2021). It derives long-side stop distance from bearish-candle ATR and short-side distance from bullish-candle ATR, which is one of the mechanisms that we tried to develop further with the KTE.
💮 Libraries Used
FiltersToolkit — Ultimate Smoother, Super Smoother, BiQuad, ADXvma, MAMA, and A2RMA
VolatilityToolkit — Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang estimators
MathTransform — Logarithmic scaling for Adaptation Speed
ColourUtilities — Palette management and light/dark-mode colour adjustment
Indicator
ValidationUtilitiesValidationUtilities Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 What Does This Library Contain?
ValidationUtilities is a centralised validation framework for Pine Script. It replaces scattered, ad-hoc input checks with a single, structured validation pass that catches every misconfiguration before a script begins operating.
The library spans the full validation workflow: framework lifecycle, configuration checks, position sizing guards, and signal completeness verification.
💮 Key Categories
The library contains:
Core Framework : the ValidationFramework UDT and its lifecycle methods (init, collect, report)
Standalone Utilities : bounded-buffer push and division-by-zero guard
Configuration Validation : range, ordering, exclusivity, lookback, source, and timeframe checks
Position Sizing & Risk : order size constraints, progressive risk alerts, allocation distribution, and Martingale safety
Signal & Timing : signal source completeness and cooldown gating
🌸 --------- 2. ADDED VALUE --------- 🌸
💮 Consistent, Readable Error Messages
Every error and warning follows the same Message format. Users see clear, categorised feedback instead of cryptic runtime error strings. A single validation pass surfaces all issues at once, so there is no need to fix one error only to hit the next on re-run.
💮 Single Import, Full Coverage
One import replaces dozens of inline validation blocks. Range checks, allocation constraints, timeframe guards, and position sizing validations are all available immediately.
💮 Errors and Warnings, Separated
Hard/soft boundary separation lets developers enforce critical constraints (errors halt execution via runtime.error() ) whilst still surfacing non-critical suggestions (warnings display as chart labels). The framework handles formatting, counting, and display.
💮 Proven in Production
ValidationUtilities underpins the validation layer of a strategy with an extensive configuration surface (12+ validated parameter groups). The methods have been refined against real misconfiguration scenarios including floating-point allocation sums, multiplier escalation, and unconnected data streams.
🌸 --------- 3. CORE FRAMEWORK --------- 🌸
💮 ValidationFramework (UDT)
The central data structure that collects validation results. It holds two string arrays, errors (critical, halt execution) and warnings (advisory, continue execution), alongside convenience flags has_errors and has_warnings .
Declare once with var , then call init() to reset state before each validation cycle:
var framework = vu.ValidationFramework.new()
framework.init()
💮 init()
Resets the framework: clears both arrays and resets flags to false . Call at the start of each validation cycle.
💮 add_error() and add_warning()
Building blocks for custom validation beyond the built-in methods. Both accept a category and message , formatting them as Message . Use add_error() for constraints that must halt execution and add_warning() for advisory messages.
framework.add_error("Position Sizing", "Order exceeds account equity.")
framework.add_warning("Risk", "Position represents 35% of equity — monitor carefully.")
💮 trigger_errors()
Fires runtime.error() with the first collected error and a count of any remaining. Always call after all validations have run so every misconfiguration is detected in a single pass.
💮 display_warnings()
Renders warnings as orange chart labels (below bar by default). Displays the first warning with a count of additional warnings, then clears state to prevent repetition. Accepts an optional yloc_arg for label placement.
↑ Runtime error dialog showing a categorised validation error with count of additional issues
↑ Warning labels displayed on the chart via display_warnings()
🌸 --------- 4. STANDALONE UTILITIES --------- 🌸
These functions are independent of the ValidationFramework and can be used anywhere.
💮 push_limited()
A FIFO bounded-buffer push: appends a value and evicts the oldest entry when the array exceeds a specified limit. Available for both float and int arrays.
vu.push_limited(price_buffer, close, 50) // Keeps the last 50 closes
💮 safe_denominator()
Returns math.max(value, floor) to guard against division by zero. Default floor is 1e-9 .
ratio = numerator / vu.safe_denominator(denominator)
🌸 --------- 5. CONFIGURATION VALIDATION --------- 🌸
These methods validate user-facing settings before a script begins operating. Each accepts the framework as self and a category string for error grouping. Refer to the source code for full parameter details.
💮 validate_range()
Checks that a value falls within hard bounds (error if violated) and optional soft bounds (warning if outside the optimal range). Supports a value_unit label for message clarity. Returns true if within hard bounds.
💮 validate_exclusive_selection()
Ensures exactly one boolean flag is active among a set of mutually exclusive options. Produces an error listing which options were found active, or that none were selected.
💮 validate_ascending_order()
Verifies that an array of values is in ascending order. Supports strict (default) or non-strict comparison. Skips na values.
💮 validate_minimum_lookback()
Checks that a lookback parameter meets a caller-derived minimum. Accepts an optional fix_hint for the error message. Returns true if met.
💮 validate_source_connected()
Detects when an input.source() has no external indicator connected (it silently defaults to close ). Uses a 2-bar close heuristic. Accepts an is_enabled flag to skip the check when the relevant feature is disabled. Returns true if the source appears connected.
💮 validate_higher_timeframe()
Validates that a user-selected timeframe is sufficiently higher than the chart timeframe. Returns the integer multiplier, useful for scaling lookback periods. Produces an error if below min_multiplier (default 1.0).
🌸 --------- 6. POSITION SIZING & RISK --------- 🌸
These methods guard against position sizing errors and excessive risk exposure. See the source code for parameter details and default thresholds.
💮 validate_order_size_constraints()
Checks a proposed order against account equity and position size limits. Errors if the order exceeds equity or a hard cap; warns if the position exceeds a configurable percentage of equity. Returns true if no errors were added.
💮 validate_multiplied_sizing_risk()
Progressive risk alerting for scripts that scale position sizes with multipliers (Martingale, Anti-Martingale, or any multiplicative sizing). Applies three escalating thresholds:
Warning (default 25%): elevated risk
Error (default 50%): high risk
Critical (default 75%): exceeds safe limits
Also warns when the multiplier itself exceeds a configurable threshold. Returns true if no errors were added.
💮 validate_martingale_settings()
Validates Martingale/Anti-Martingale parameter consistency: multiplier range, streak bounds, and maximum possible escalation. Warns when maximum escalation exceeds 100×.
💮 validate_allocations()
Validates percentage distributions (0–1 scale) for take-profit levels, portfolio weights, or any system that divides a whole into parts. Checks individual allocations and total against 1.0 with floating-point tolerance. Supports both mandatory full allocation and partial allocation.
🌸 --------- 7. SIGNAL & TIMING --------- 🌸
These methods verify signal completeness and enforce cooldown periods. See the source code for parameter details.
💮 validate_signal_configuration()
Completeness check for signal sources. Validates that an enabled signal has a connected primary data stream, a secondary stream (if required), at least one signal mapping, and activity in at least one market regime (when regime filtering is enabled).
💮 validate_timing_cooldown()
Gating check for entry timing. Verifies that enough bars have elapsed since the last relevant event and that a valid entry signal is present. Both conditions produce warnings rather than errors.
🌸 --------- 8. USAGE EXAMPLE --------- 🌸
A typical validation lifecycle: import, initialise, run validations, then trigger errors and display warnings.
import GoemonYae/ValidationUtilities/1 as vu
// Declare once, reset each bar
var framework = vu.ValidationFramework.new()
framework.init()
// Configuration validation
framework.validate_range("Config", "ATR Lookback", i_atr_lookback, 1, 500, 10, 50, "bars")
framework.validate_exclusive_selection("Distance", "TP Mode",
array.from(i_use_pct, i_use_atr, i_use_hl),
array.from("Percentage", "ATR", "High/Low"), "method")
// Allocation validation
framework.validate_allocations("TP Settings", "Take Profit",
array.from(i_tp1_alloc, i_tp2_alloc, i_tp3_alloc),
array.from("TP1", "TP2", "TP3"), true)
// Position sizing guard
framework.validate_order_size_constraints("Sizing",
order_size, close, strategy.equity, max_pos, 50.0)
// Report results
framework.trigger_errors() // Halts if any errors found
framework.display_warnings() // Shows warnings on chart
When all inputs are valid, trigger_errors() does nothing and execution continues; display_warnings() draws no labels. A correctly configured script simply runs with a clean chart.
🌸 --------- 9. PRACTICAL USAGE NOTES --------- 🌸
💮 Errors vs Warnings
Use add_error() for constraints that make the script unsafe or logically broken (missing data streams, impossible parameter combinations, equity-exceeding orders). Use add_warning() for suboptimal but non-dangerous configurations (values outside the recommended range, elevated risk percentages). Errors halt execution; warnings inform via chart labels.
💮 Single-Pass Collection
Always run all validations before calling trigger_errors() . The framework collects every error in a single pass so the user sees the total count of issues.
💮 Integration with Other GYTS Libraries
ValidationUtilities complements the GYTS library ecosystem:
FiltersToolkit : smoothing and signal processing
VolatilityToolkit : volatility estimation and regime detection
ColourUtilities : dynamic colour mapping
MathTransform : mathematical transformations and normalisation
Each library handles its own domain; ValidationUtilities handles the validation layer that sits above them.
💮 Limitations
A few constraints to keep in mind:
The validate_source_connected() heuristic (2-bar close comparison) can produce false positives if a source genuinely tracks price closely. It is a best-effort detection, not a guarantee.
Pine Script libraries cannot import other libraries. So ValidationUtilities is designed for indicators and strategies.
The framework validates configuration state, not runtime state. It catches misconfigurations at the input level; it does not monitor runtime behaviour.
Library
[GYTS-CE] Pattern Texture Codex (PTC)Pattern Texture Codex (Community Edition)
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What is the Pattern Texture Codex?
Standard technical analysis focuses on two dimensions: Amplitude (how far price moves) and Momentum (how fast price moves). The Pattern Texture Codex introduces a third: Structure (how price moves).
This indicator implements Permutation Entropy (PE), a complexity measure from dynamical systems theory that captures whether price evolves in structured patterns or chaotic noise. We call this "Market Texture":
🫧 Smooth Texture (Low Entropy): Price evolves in ordered, predictable patterns. Trends are durable and causality is high. Momentum strategies favoured.
🌵 Rough Texture (High Entropy): Price evolves chaotically. The market is noisy, trends are fragile. Mean reversion or defensive sizing recommended.
💮 Why Use This Indicator?
Most "entropy" indicators on PulseWire fall into common traps:
Shannon entropy of price histograms — measures value distribution but ignores temporal sequence
Approximate Entropy (ApEn) — measures amplitude similarity with O(N²) computational cost
Volatility metrics labelled "entropy" — captures magnitude, not pattern structure
Mathematical errors — normalised values that don't form valid probability distributions
The Pattern Texture Codex provides true ordinal pattern analysis — it examines the sequence of price movements, not just their distribution or magnitude. A smooth uptrend and choppy consolidation may have identical volatility, but their texture is completely different.
↑ Pattern Texture Codex with dynamic threshold bands. Rough Texture (high entropy) often indicates reversals, while Smooth Texture (low entropy) often precedes trend continuation.
🌸 --------- HOW IT WORKS --------- 🌸
💮 Core Concept: Ordinal Patterns
Instead of analysing raw price values, Permutation Entropy converts price into ordinal patterns — the relative ordering of consecutive data points.
For example, with embedding dimension D=3 (three points per pattern):
Pattern "012": first < second < third → ascending
Pattern "210": first > second > third → descending
Pattern "102": middle value smallest → valley shape
The indicator counts how often each pattern appears over a lookback window, then calculates the Shannon entropy of this distribution.
↑ With D=3, three consecutive data points determine each pattern. Left: ascending pattern "012" (first point smallest, second middle, third greatest). Right: descending pattern "210" (first point greatest, second middle, third smallest).
💮 Calculation Overview
The normalised Permutation Entropy is computed as:
H = −∑ p(π) · ln(p(π)) / ln(D!)
Where:
• p(π) is the probability of each ordinal pattern π
• D is the embedding dimension (number of points per pattern)
• D! is the total possible patterns (e.g., 4! = 24 for D=4)
The result ranges from 0 to 1:
• H → 0 : One pattern dominates — highly structured, predictable
• H → 1 : All patterns equally likely — pure randomness
↑ Full calculation example at D=3 showing the lowest entropy point (green vertical line). With 3!=6 possible patterns, the monotonic rising pattern "012" dominates while three other patterns occur only once. The frequency column feeds into the entropy contribution formula, yielding H(3)=1.039. Normalising produces 0.4019 — matching the indicator output exactly.
💮 Theoretical Background
Permutation Entropy has deep theoretical foundations. For piecewise monotone maps, it converges to the Kolmogorov-Sinai entropy — the fundamental measure of chaos in dynamical systems.
Key scientific properties:
• Scale invariance — analyses rank orderings, invariant to monotonic transformations
• Noise robustness — ordinal encoding naturally filters high-frequency noise
• Computational efficiency — O(1) amortised per bar with lookup acceleration
• Micro-structure sensitivity — captures specific sequence patterns, not just distribution
🌸 --------- KEY FEATURES --------- 🌸
💮 Lookup Table Acceleration
Standard PE requires sorting each embedding vector — O(D log D) operations per bar. This implementation uses precomputed transition tables from Unakafova & Keller (2013), reducing complexity to O(D) per bar.
The key insight: successive ordinal patterns in overlapping windows share (D−1) data points. Rather than recomputing from scratch, the algorithm derives the new pattern from the previous one using a single table lookup.
Enabled by default for Delay=1 and Dimension ∈ {3, 4, 5}
Falls back to standard calculation for D=2, D=6
💮 Flexible Threshold Modes
The indicator supports four independent threshold modes for both Smooth and Rough detection:
Static — Fixed threshold values you define
Dynamic — Adaptive bands based on entropy baseline ± standard deviation
Percentile — Threshold at Nth percentile of recent entropy history
Disabled — No threshold for that direction
You can mix modes: for example, Dynamic for Smooth detection while using Percentile for Rough detection.
🌸 --------- CONFIGURATION --------- 🌸
💮 General Settings
• Source — Price series to analyse (default: close)
• Smoothing Critical Period — Smoothing via 2-pole Ultimate Smoother (default: 0 = disabled). Reveals underlying texture by filtering entropy noise.
💮 Entropy Calculation
Dimension (D) — Points per ordinal pattern:
• D=3: 6 patterns — fast, stable. Good for limited lookback.
• D=4: 24 patterns — balanced, captures V-reversals. Recommended.
• D=5: 120 patterns — sensitive, captures W/M patterns. Noisier.
• D=6: 720 patterns — maximum sensitivity. No lookup acceleration.
Lookback — Estimation window size. Hard minimum: D × 5. Statistical recommendation: 5 × D! (e.g., 120 for D=4). Default: 100.
Delay (τ) — Stride between points in each pattern (default: 1). Change only for oversampled data.
Lookup Acceleration — Enables transition tables for D ∈ {3, 4, 5} with Delay=1.
💮 Threshold Management
Rough/Smooth Mode — Static, Dynamic, Percentile, or Disabled for each threshold
Static Values — Fixed threshold when Static mode selected
Std Dev Multiplier — Band width for Dynamic mode (default: 2.0σ)
Baseline/Deviation Length — Lookback for Dynamic mode calculations
Percentile Settings — Lookback and percentile values for Percentile mode
💮 Visualisation & Alerts
Palette — Colour scheme (default: GYTS Purple)
Colouring Bars — Applies texture colours to chart candles
Dark Mode — Optimises colour intensity for dark backgrounds
Alerts — Triggers when entropy crosses above/below thresholds
🌸 --------- USAGE GUIDE --------- 🌸
💮 Getting Started
Apply the indicator with default settings:
• Dimension: 4 (balanced complexity, captures V-shaped reversals)
• Lookback: 100 (responsive; statistical ideal: ≥120 for 5× coverage)
• Smooth Threshold: Dynamic mode with 2.0σ multiplier
Observe how entropy rises during choppy consolidation and falls during clean trends.
💮 Interpretation
Entropy Value (0 to 1):
Below 0.6: Strong pattern dominance — highly ordered
0.7–0.9: Normal complexity — typical market behaviour
Above 0.95: Near-random — patterns uniformly distributed
Transitions:
Watch for regime changes. When entropy rises sharply after a prolonged smooth period, the trend may be losing coherence. When entropy falls from elevated levels, a new trend may be establishing.
↑ Texture transitions during a trend-to-consolidation regime change. During the uptrend, similar patterns (D=3) recur frequently and entropy decreases. As the market transitions to consolidation, entropy rises — signalling the trend is losing structure.
💮 Trading Applications
Trend Filtering — Only take trend-following signals during Smooth texture.
Mean Reversion Timing — Elevated entropy often precedes mean reversion.
Position Sizing — Reduce exposure during Rough texture.
Exit Management — Tighten stops when entropy rises during a position.
💮 Integration with GYTS Suite
The Pattern Texture Codex exports two signals:
PE Continuous — Raw entropy value (0 to 1)
PE Ternary — State signal (+1 = Rough, 0 = Neutral, −1 = Smooth)
These can be read by Flux Composer or used as filter conditions with Market Regime Detector .
🌸 --------- PARAMETER TUNING --------- 🌸
💮 Lookback Selection
Shorter lookbacks react faster but may produce unstable estimates:
50–100: Responsive. Good for intraday regime detection.
100–200: Balanced. Recommended for swing trading.
200–500: Stable. Better for position trading or noisy instruments.
The indicator enforces a hard minimum of D × 5 to prevent meaningless output.
↑ Three dimensions (D=3, D=4, D=5) with their academically recommended minimum lookback periods.
💮 Threshold Tuning
For Smooth Detection:
Dynamic mode with 2.0σ works well across most instruments. Lower multipliers (1.5σ) detect structure earlier but may false-trigger.
For Rough Detection:
Percentile mode at 90th percentile identifies only extreme chaos. Static threshold of 0.95+ focuses on near-random conditions.
Consider disabling Rough detection entirely if your strategy only cares about identifying structured trends.
↑ The three threshold modes on the same PTC calculation. Both upper and lower thresholds are independently configurable.
🌸 --------- LIMITATIONS --------- 🌸
Amplitude Blindness — PE treats all patterns equally regardless of magnitude. A 0.1% drift and a 10% crash produce identical entropy if their ordinal patterns match.
Equal Values (Ties) — Handled via temporal tie-breaking (recent values rank higher), but heavily discretised data may produce edge-case behaviour.
Sample Size Requirements — Very short lookbacks (below D × 5) produce unreliable estimates. Statistical reliability improves with larger samples.
Not Predictive Alone — Low entropy indicates structure exists, not that the trend will continue. Combine with directional analysis for trading decisions.
Lag During Transitions — The sliding window approach introduces inherent lag when market texture changes.
🌸 --------- CREDITS --------- 🌸
💮 Academic Sources
Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88 (17), 174102. DOI
Unakafova, V., & Keller, K. (2013). Efficiently measuring complexity on the basis of real-world data. Entropy, 15 (10), 4392-4415. DOI
Ehlers, J. F. (2024). The Ultimate Smoother. Technical Analysis of Stocks & Commodities , 2024-04. TASC
💮 Libraries Used
FiltersToolkit — Ultimate Smoother and other curated filters
PatternTransitionTables — Precomputed lookup tables for O(1) pattern transitions
ColourUtilities — Gradient palette generation and colour management
Indicator
[GYTS] Volatility Toolkit Volatility Toolkit
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What is Volatility Toolkit?
Volatility Toolkit is a comprehensive volatility analysis indicator featuring academically-grounded range-based estimators. Unlike simplistic measures like ATR, these estimators extract maximum information from OHLC data — resulting in estimates that are 5-14× more statistically efficient than traditional close-to-close methods.
The indicator provides two configurable estimator slots, weighted aggregation, adaptive threshold detection, and regime identification — all with flexible smoothing options via
GYTS FiltersToolkit integration.
💮 Why Use This Indicator?
Standard volatility measures (like simple standard deviation) are highly inefficient, requiring large amounts of data to produce stable estimates. Academic research has shown that range-based estimators extract far more information from the same price data:
• Statistical Efficiency — Yang-Zhang achieves up to 14× the efficiency of close-to-close variance, meaning you can achieve the same estimation accuracy with far fewer bars
• Drift Independence — Rogers-Satchell and Yang-Zhang correctly isolate variance even in strongly trending markets where simpler estimators become biased
• Gap Handling — Yang-Zhang properly accounts for overnight gaps, critical for equity markets
• Regime Detection — Built-in threshold modes identify when volatility enters elevated or suppressed states
↑ Overview showing Yang-Zhang volatility with dynamic threshold bands and regime background colouring
🌸 --------- HOW IT WORKS --------- 🌸
💮 Core Concept
The toolkit groups volatility estimators by their output scale to ensure valid comparisons and aggregations:
• Log-Return Scale (σ) — Close-to-Close, Parkinson, Garman-Klass, Rogers-Satchell, Yang-Zhang. These are comparable and can be aggregated. Annualisable via √(periods_per_year) scaling.
• Price Unit Scale ($) — ATR. Measures volatility in absolute price terms, directly usable for stop-loss placement.
• Percentage Scale (%) — Chaikin Volatility. Measures the rate of change of the trading range — whether volatility is expanding or contracting.
Only estimators with the same scale can be meaningfully compared or aggregated. The indicator enforces this and warns when mixing incompatible scales.
💮 Range-Based Estimator Overview
Range-based estimators utilise High, Low, Open, and Close prices to extract significantly more information about the underlying diffusion process than close-only methods:
• Parkinson (1980) — Uses High-Low range. ~5× more efficient than close-to-close. Assumes zero drift.
• Garman-Klass (1980) — Incorporates Open and Close. ~7.4× more efficient. Assumes zero drift, no gaps.
• Rogers-Satchell (1991) — Drift-independent. Superior in trending markets where Parkinson/GK become biased.
• Yang-Zhang (2000) — Composite estimator handling both drift and overnight gaps. Up to 14× more efficient.
💮 Theoretical Background
• Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53 (1), 61–65. DOI
• Garman, M.B. & Klass, M.J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53 (1), 67–78. DOI
• Rogers, L.C.G. & Satchell, S.E. (1991). Estimating Variance from High, Low and Closing Prices. Annals of Applied Probability, 1 (4), 504–512. DOI
• Yang, D. & Zhang, Q. (2000). Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices. Journal of Business, 73 (3), 477–491. DOI
🌸 --------- KEY FEATURES --------- 🌸
💮 Feature Reference
Estimators (8 options across 3 scale groups):
• Close-to-Close — Classical benchmark using closing prices only. Least efficient but useful as baseline. Log-return scale.
• Parkinson — Range-based (High-Low), ~5× more efficient than close-to-close. Assumes zero drift. Log-return scale.
• Garman-Klass — OHLC-optimised, ~7.4× more efficient. Assumes zero drift, no gaps. Log-return scale.
• Rogers-Satchell — Drift-independent, handles trending markets where Parkinson/GK become biased. Log-return scale.
• Yang-Zhang — Gap-aware composite, most comprehensive (up to 14× efficient). Uses internal rolling variance (unsmoothed). Log-return scale.
• Std Dev — Standard deviation of log returns. Log-return scale.
• ATR — Average True Range in absolute price units. Useful for stop-loss placement. Price unit scale.
• Chaikin — Rate of change of range. Measures volatility expansion/contraction, not level. Percentage scale.
Smoothing Filters (10 options via FiltersToolkit):
• SMA / EMA — Classical moving averages
• Super Smoother (2-Pole / 3-Pole) — Ehlers IIR filter with excellent noise reduction
• Ultimate Smoother (2-Pole / 3-Pole) — Near-zero lag in passband
• BiQuad — Second-order IIR with configurable Q factor
• ADXvma — Adaptive smoothing, flat during ranging periods
• MAMA — MESA Adaptive Moving Average (cycle-adaptive)
• A2RMA — Adaptive Autonomous Recursive MA
Threshold Modes:
• Static — Fixed threshold values you define (e.g., 0.025 annualised)
• Dynamic — Adaptive bands: baseline ± (standard deviation × multiplier)
• Percentile — Threshold at Nth percentile of recent history (e.g., 80th percentile for high)
Visual Features:
• Level-based colour gradient — Line colour shifts with percentile rank (warm = high vol, cool = low vol)
• Fill to zero — Gradient fill intensity proportional to volatility level
• Threshold fills — Intensity-scaled fills when thresholds are breached
• Regime background — Chart background indicates HIGH/NORMAL/LOW volatility state
• Legend table — Displays estimator names, parameters, current values with percentile ranks (P##)
💮 Dual Estimator Slots
Compare two volatility estimators side-by-side. Each slot independently configures:
• Estimator type (8 options across three scale groups)
• Lookback period and smoothing filter
• Colour palette and visual style
This enables direct comparison between estimators (e.g., Yang-Zhang vs Rogers-Satchell) or between different parameterisations of the same estimator.
↑ Yang-Zhang (reddish) and Rogers-Satchell (greenish)
💮 Flexible Smoothing via FiltersToolkit
All estimators (except Yang-Zhang, which uses internal rolling variance) support configurable smoothing through 10 filter types. Using Infinite Impulse Response (IIR) filters instead of SMA avoids the "drop-off artefact" where volatility readings crash when old spikes exit the window.
Example: Same estimator (Parkinson) with different smoothing filters
Add two instances of Volatility Toolkit to your chart:
• Instance 1: Parkinson with SMA smoothing (lookback 14)
• Instance 2: Parkinson with Super Smoother 2-Pole (lookback 14)
Notice how SMA creates sharp drops when volatile bars exit the window, while Super Smoother maintains a gradual transition.
↑ Two Parkinson estimators — SMA (red mono-colour, showing drop-off artefacts) vs Super Smoother (turquoise mono colour, with smooth transitions)
↑ Garman-Klass with BiQuad (orangy) and 2-pole SuperSmoother filters (greenish)
💮 Weighted Aggregation
Combine multiple estimators into a single weighted average. The indicator automatically:
• Validates scale compatibility (only same-scale estimators can be aggregated)
• Normalises weights (so 2:1 means 67%:33%)
• Displays clear warnings when scales differ
Example: Robust volatility estimate
Combine Yang-Zhang (handles gaps) with Rogers-Satchell (handles drift) using equal weights:
• E1: Yang-Zhang (14)
• E2: Rogers-Satchell (14)
• Aggregation: Enabled, weights 1:1
The aggregated line (with "fill to zero" enabled) provides a more robust estimate by averaging two complementary methodologies.
↑ Yang-Zhang + Rogers-Satchell with aggregation line (thicker) showing combined estimate (notice how opening gaps are handled differently)
Example: Trend-weighted aggregation
In strongly trending markets, weight Rogers-Satchell more heavily since it's drift-independent:
• Estimator 1: Garman-Klass (faster, higher weight in ranging)
• Estimator 2: Rogers-Satchell (drift-independent, higher weight in trends)
• Aggregation: weights 1:2 (favours RS during trends)
💮 Adaptive Threshold Detection
Three threshold modes for identifying volatility regime shifts. Threshold breaches are visualised with intensity-scaled fills that grow stronger the further volatility exceeds the threshold.
Example: Dynamic thresholds for regime detection
Configure dynamic thresholds to automatically adapt to market conditions:
• High Threshold Mode: Dynamic (baseline + 2× std dev)
• Low Threshold Mode: Dynamic (baseline - 2× std dev)
• Show threshold fills: Enabled
This creates adaptive bands that widen during volatile periods and narrow during calm periods.
Example: Percentile-based thresholds
Use percentile mode for context-aware regime detection:
• High Threshold Mode: Percentile (96th)
• Low Threshold Mode: Percentile (4th)
• Percentile Lookback: 500
This identifies when volatility enters the top/bottom 4% of its recent distribution.
↑ Different threshold settings, where the dynamic and percentile methods show adaptive bands that widen during volatile periods, with fill intensity varying by breach magnitude. Regime detection (see next) is enabled too.
💮 Regime Background Colouring
Optional background colouring indicates the current volatility regime:
• High Volatility — Warm/alert background colour
• Normal — No background (neutral)
• Low Volatility — Cool/calm background colour
Select which source (Estimator 1, Estimator 2, or Aggregation) drives the regime display.
Example: Regime filtering for trade decisions
Use regime background to filter trading signals from other indicators:
• Regime Source: Aggregation
• Background Transparency: 90 (subtle)
When the background shows HIGH volatility (warm), consider tighter stops. When LOW (cool), watch for breakout setups.
↑ Regime background emphasis for breakout strategies. Note the interesting A2RMA smoothing for this case.
🌸 --------- USAGE GUIDE --------- 🌸
💮 Getting Started
1. Add the indicator to your chart
2. Estimator 1 defaults to Yang-Zhang (14) — the most comprehensive estimator for gapped markets
3. Keep "Annualise Volatility" enabled to express values in standard annualised form
4. Observe the legend table for current values and percentile ranks (P##). Hover over the table cells to see a little more info in the tooltip.
💮 Choosing an Estimator
• Trending equities with gaps — Yang-Zhang. Handles both drift and overnight gaps optimally.
• Crypto (24/7 trading) — Rogers-Satchell. Drift-independent without Yang-Zhang's multi-period lag.
• Ranging markets — Garman-Klass or Parkinson. Simpler, no drift adjustment needed.
• Price-based stops — ATR. Output in price units, directly usable for stop distances.
• Regime detection — Combine any estimator with threshold modes enabled.
💮 Interpreting Output
• Value (P##) — The volatility reading with percentile rank. "0.1523 (P75)" means 0.1523 annualised volatility at the 75th percentile of recent history.
• Colour gradient — Warmer colours = higher percentile (elevated volatility), cooler colours = lower percentile.
• Threshold fills — Intensity indicates how far beyond the threshold the current reading is.
• ⚠️ HIGH / 🔻 LOW — Table indicators when thresholds are breached.
🌸 --------- ALERTS --------- 🌸
💮 Direction Change Alerts
• Estimator 1/2 direction change — Triggers when volatility inflects (rising to falling or vice versa)
💮 Cross Alerts
• E1 crossed E2 — Triggers when the two estimator lines cross
💮 Threshold Alerts
• E1/E2/Aggr High Volatility — Triggers when volatility breaches the high threshold
• E1/E2/Aggr Low Volatility — Triggers when volatility falls below the low threshold
💮 Regime Change Alerts
• E1/E2/Aggr Regime Change — Triggers when the volatility regime transitions (High ↔ Normal ↔ Low)
🌸 --------- LIMITATIONS --------- 🌸
• Drift bias in Parkinson/GK — These estimators overestimate variance in trending conditions. Switch to Rogers-Satchell or Yang-Zhang for trending markets.
• Yang-Zhang minimum lookback — Requires at least 2 bars (enforced internally). Cannot produce instantaneous readings like other estimators.
• Flat candles — Single-tick bars produce near-zero variance readings. Use higher timeframes for illiquid assets.
• Discretisation bias — Estimates degrade when ticks-per-bar is very small. Consider higher timeframes for thinly traded instruments.
• Scale mixing — Different scale groups (log-return, price unit, percentage) cannot be meaningfully compared or aggregated. The indicator warns but does not prevent display.
🌸 --------- CREDITS --------- 🌸
💮 Academic Sources
• Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53 (1), 61–65. DOI
• Garman, M.B. & Klass, M.J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53 (1), 67–78. DOI
• Rogers, L.C.G. & Satchell, S.E. (1991). Estimating Variance from High, Low and Closing Prices. Annals of Applied Probability, 1 (4), 504–512. DOI
• Yang, D. & Zhang, Q. (2000). Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices. Journal of Business, 73 (3), 477–491. DOI
• Wilder, J.W. (1978). New Concepts in Technical Trading Systems . Trend Research.
💮 Libraries Used
• VolatilityToolkit Library — Range-based estimators, smoothing, and aggregation functions
• FiltersToolkit Library — Advanced smoothing filters (Super Smoother, Ultimate Smoother, BiQuad, etc.)
• ColourUtilities Library — Colour palette management and gradient calculations Indicator
[GYTS] VolatilityToolkit LibraryVolatilityToolkit Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What Does This Library Contain?
VolatilityToolkit provides a comprehensive suite of volatility estimation functions derived from academic research in financial econometrics. Rather than relying on simplistic measures, this library implements range-based estimators that extract maximum information from OHLC data — delivering estimates that are 5–14× more efficient than traditional close-to-close methods.
The library spans the full volatility workflow: estimation, smoothing, and regime detection.
💮 Key Categories
• Range-Based Estimators — Parkinson, Garman-Klass, Rogers-Satchell, Yang-Zhang (academically-grounded variance estimators)
• Classical Measures — Close-to-Close, ATR, Chaikin Volatility (baseline and price-unit measures)
• Smoothing & Post-Processing — Asymmetric EWMA for differential decay rates
• Aggregation & Regime Detection — Multi-horizon blending, MTF aggregation, Volatility Burst Ratio
💮 Originality
To the best of our knowledge, no other PulseWire script combines range-based estimators (Parkinson, Garman-Klass, Rogers-Satchell, Yang-Zhang), classical measures, and regime detection tools in a single package. Unlike typical volatility implementations that offer only a single method, this library:
• Implements four academically-grounded range-based estimators with proper mathematical foundations
• Handles drift bias and overnight gaps, issues that plague simpler estimators in trending markets
• Integrates with GYTS FiltersToolkit for advanced smoothing (10 filter types vs. typical SMA-only)
• Provides regime detection tools (Burst Ratio, MTF aggregation) for systematic strategy integration
• Standardises output units for seamless estimator comparison and swapping
🌸 --------- ADDED VALUE --------- 🌸
💮 Academic Rigour
Each estimator implements peer-reviewed methodologies with proper mathematical foundations. The library handles aspects that are easily missed, e.g. drift independence, overnight gap adjustment, and optimal weighting factors. All functions include guards against edge cases (division by zero, negative variance floors, warmup handling).
💮 Statistical Efficiency
Range-based estimators extract more information from the same data. Yang-Zhang achieves up to 14× the efficiency of close-to-close variance, meaning you can achieve the same estimation accuracy with far fewer bars — critical for adapting quickly to changing market conditions.
💮 Flexible Smoothing
All estimators support configurable smoothing via the GYTS FiltersToolkit integration. Choose from 10 filter types to balance responsiveness against noise reduction:
• Ultimate Smoother (2-Pole / 3-Pole) — Near-zero lag; the 3-pole variant is a GYTS design with tunable overshoot
• Super Smoother (2-Pole / 3-Pole) — Excellent noise reduction with minimal lag
• BiQuad — Second-order IIR filter with quality factor control
• ADXvma — Adaptive smoothing based on directional volatility
• MAMA — Cycle-adaptive moving average
• A2RMA — Adaptive autonomous recursive moving average
• SMA / EMA — Classical averages (SMA is default for most estimators)
Using Infinite Impulse Response (IIR) filters (e.g. Super Smoother, Ultimate Smoother) instead of SMA avoids the "drop-off artefact" where volatility readings crash when old spikes exit the window.
💮 Plug-and-Play Integration
Standardised output units (per-bar log-return volatility) make it trivial to swap estimators. The annualize() helper converts to yearly volatility with a single call. All functions work seamlessly with other GYTS components.
🌸 --------- RANGE-BASED ESTIMATORS --------- 🌸
These estimators utilise High, Low, Open, and Close prices to extract significantly more information about the underlying diffusion process than close-only methods.
💮 parkinson()
The Extreme Value Method -- approximately 5× more efficient than close-to-close, requiring about 80% less data for equivalent accuracy. Uses only the High-Low range, making it simple and robust.
• Assumption: Zero drift (random walk). May be biased in strongly trending markets.
• Best for: Quick volatility reads when drift is minimal.
• Parameters: smoothing_length (default 14), filter_type (default SMA), smoothing_factor (default 0.7)
Source: Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53 (1), 61–65. DOI
💮 garman_klass()
Extends Parkinson by incorporating Open and Close prices, achieving approximately 7.4× efficiency over close-to-close. Implements the "practical" analytic estimator (σ̂²₅) which avoids cross-product terms whilst maintaining near-optimal efficiency.
• Assumption: Zero drift, continuous trading (no gaps).
• Best for: Markets with minimal overnight gaps and ranging conditions.
• Parameters: smoothing_length (default 14), filter_type (default SMA), smoothing_factor (default 0.7)
Source: Garman, M.B. & Klass, M.J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53 (1), 67–78. DOI
💮 rogers_satchell()
The drift-independent estimator correctly isolates variance even in strongly trending markets where Parkinson and Garman-Klass become significantly biased. Uses the formula: ln(H/C)·ln(H/O) + ln(L/C)·ln(L/O).
• Key advantage: Unbiased regardless of trend direction or magnitude.
• Best for: Trending markets, crypto (24/7 trading with minimal gaps), general-purpose use.
• Parameters: smoothing_length (default 14), filter_type (default SMA), smoothing_factor (default 0.7)
Source: Rogers, L.C.G. & Satchell, S.E. (1991). Estimating Variance from High, Low and Closing Prices. Annals of Applied Probability, 1 (4), 504–512. DOI
💮 yang_zhang()
The minimum-variance composite estimator — both drift-independent AND gap-aware. Combines overnight returns, open-to-close returns, and the Rogers-Satchell component with optimal weighting to minimise estimator variance. Up to 14× more efficient than close-to-close.
• Parameters: lookback (default 14, minimum 2), alpha (default 1.34, optimised for equities).
• Best for: Equity markets with significant overnight gaps, highest-quality volatility estimation.
• Note: Unlike other estimators, Yang-Zhang does not support custom filter types — it uses rolling sample variance internally.
Source: Yang, D. & Zhang, Q. (2000). Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices. Journal of Business, 73 (3), 477–491. DOI
🌸 --------- CLASSICAL MEASURES --------- 🌸
💮 close_to_close()
Classical sample variance of logarithmic returns. Provided primarily as a baseline benchmark — it is approximately 5–8× less efficient than range-based estimators, requiring proportionally more data for the same accuracy.
• Parameters: lookback (default 14), filter_type (default SMA), smoothing_factor (default 0.7)
• Use case: Comparison baseline, situations requiring strict methodological consistency with academic literature.
💮 atr()
Average True Range -- measures volatility in price units rather than log-returns. Directly interpretable for stop-loss placement (e.g., "2× ATR trailing stop") and handles gaps naturally via the True Range formula.
• Output: Price units (not comparable across different price levels).
• Parameters: smoothing_length (default 14), filter_type (default SMA), smoothing_factor (default 0.7)
• Best for: Position sizing, trailing stops, any application requiring volatility in currency terms.
Source: Wilder, J.W. (1978). New Concepts in Technical Trading Systems . Trend Research.
💮 chaikin_volatility()
Rate of Change of the smoothed trading range. Unlike level-based measures, Chaikin Volatility shows whether volatility is expanding or contracting relative to recent history.
• Output: Percentage change (oscillates around zero).
• Parameters: length (default 10), roc_length (default 10), filter_type (default EMA), smoothing_factor (default 0.7)
• Interpretation: High values suggest nervous, wide-ranging markets; low values indicate compression.
• Best for: Detecting volatility regime shifts, breakout anticipation.
🌸 --------- SMOOTHING & POST-PROCESSING --------- 🌸
💮 asymmetric_ewma()
Differential smoothing with separate alphas for rising versus falling volatility. Allows volatility to spike quickly (fast reaction to shocks) whilst decaying slowly (stability). Essential for trailing stops that should widen rapidly during turbulence but narrow gradually.
• Parameters: alpha_up (default 0.1), alpha_down (default 0.02).
• Note: Stateful function — call exactly once per bar.
💮 annualize()
Converts per-bar volatility to annualised volatility using the square-root-of-time rule: σ_annual = σ_bar × √(periods_per_year).
• Parameters: vol (series float), periods (default 252 for daily equity bars).
• Common values: 365 (crypto), 52 (weekly), 12 (monthly).
🌸 --------- AGGREGATION & REGIME DETECTION --------- 🌸
💮 weighted_horizon_volatility()
Blends volatility readings across short, medium, and long lookback horizons. Inspired by the Heterogeneous Autoregressive (HAR-RV) model's recognition that market participants operate on different time scales.
• Default horizons: 1-bar (short), 5-bar (medium), 22-bar (long).
• Default weights: 0.5, 0.3, 0.2.
• Note: This is a weighted trailing average, not a forecasting regression. For true HAR-RV forecasting, it would be required to fit regression coefficients.
Inspired by: Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics .
💮 volatility_mtf()
Multi-timeframe aggregation for intraday charts. Combines base volatility with higher-timeframe (Daily, Weekly, Monthly) readings, automatically scaling HTF volatilities down to the current timeframe's magnitude using the square-root-of-time rule.
• Usage: Calculate HTF volatilities via request.security() externally, then pass to this function.
• Behaviour: Returns base volatility unchanged on Daily+ timeframes (MTF aggregation not applicable).
💮 volatility_burst_ratio()
Regime shift detector comparing short-term to long-term volatility.
• Parameters: short_period (default 8), long_period (default 50), filter_type (default Super Smoother 2-Pole), smoothing_factor (default 0.7)
• Interpretation: Ratio > 1.0 indicates expanding volatility; values > 1.5 often precede or accompany explosive breakouts.
• Best for: Filtering entries (e.g., "only enter if volatility is expanding"), dynamic risk adjustment, breakout confirmation.
🌸 --------- PRACTICAL USAGE NOTES --------- 🌸
💮 Choosing an Estimator
• Trending equities with gaps: yang_zhang() — handles both drift and overnight gaps optimally.
• Crypto (24/7 trading): rogers_satchell() — drift-independent without the lag of Yang-Zhang's multi-period window.
• Ranging markets: garman_klass() or parkinson() — simpler, no drift adjustment needed.
• Price-based stops: atr() — output in price units, directly usable for stop distances.
• Regime detection: Combine any estimator with volatility_burst_ratio().
💮 Output Units
All range-based estimators output per-bar volatility in log-return units (standard deviation). To convert to annualised percentage volatility (the convention in options and risk management), use:
vol_annual = annualize(yang_zhang(14), 252) // For daily bars
vol_percent = vol_annual * 100 // Express as percentage
💮 Smoothing Selection
The library integrates with FiltersToolkit for flexible smoothing. General guidance:
• SMA: Classical, statistically valid, but suffers from "drop-off" artefacts when spikes exit the window.
• Super Smoother / Ultimate Smoother / BiQuad: Natural decay, reduced lag — preferred for trading applications.
• MAMA / ADXvma / A2RMA: Adaptive smoothing, sometimes interesting for highly dynamic environments.
💮 Edge Cases and Limitations
• Flat candles: Guards prevent log(0) errors, but single-tick bars produce near-zero variance readings.
• Illiquid assets: Discretisation bias causes underestimation when ticks-per-bar is small. Use higher timeframes for more reliable estimates.
• Yang-Zhang minimum: Requires lookback ≥ 2 (enforced internally). Cannot produce instantaneous readings.
• Drift in Parkinson/GK: These estimators overestimate variance in trending conditions — switch to Rogers-Satchell or Yang-Zhang.
Note: This library is actively maintained. Suggestions for additional estimators or improvements are welcome. Library
PatternTransitionTablesPatternTransitionTables Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 Overview
This library provides precomputed state transition tables to enable ultra-efficient, O(1) computation of Ordinal Patterns. It is designed specifically to support high-performance indicators calculating Permutation Entropy and related complexity measures.
💮 The Problem & Solution
Calculating Permutation Entropy, as introduced by Bandt and Pompe (2002), typically requires computing ordinal patterns within a sliding window at every time step. The standard successive-pattern method (Equations 2+3 in the paper) requires ≤ 4d-1 operations per update.
Unakafova and Keller (2013) demonstrated that successive ordinal patterns "overlap" significantly. By knowing the current pattern index and the relative rank (position l) of just the single new data point, the next pattern index can be determined via a precomputed look-up table. Computing l still requires d comparisons, but the table lookup itself is O(1), eliminating the need for d multiplications and d additions. This reduces total operations from ≤ 4d-1 to ≤ 2d per update (Table 4). This library contains these precomputed tables for orders d = 2 through d = 5.
🌸 --------- 2. THEORETICAL BACKGROUND --------- 🌸
💮 Permutation Entropy
Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series.
doi.org
This concept quantifies the complexity of a system by comparing the order of neighbouring values rather than their magnitudes. It is robust against noise and non-linear distortions, making it ideal for financial time series analysis.
💮 Efficient Computation
Unakafova, V. A., & Keller, K. (2013). Efficiently Measuring Complexity on the Basis of Real-World Data.
doi.org
This library implements the transition function φ_d(n, l) described in Equation 5 of the paper. It maps a current pattern index (n) and the position of the new value (l) to the successor pattern, reducing the complexity of updates to constant time O(1).
🌸 --------- 3. LIBRARY FUNCTIONALITY --------- 🌸
💮 Data Structure
The library stores transition matrices as flattened 1D integer arrays. These tables are mathematically rigorous representations of the factorial number system used to enumerate permutations.
💮 Core Function: get_successor()
This is the primary interface for the library for direct pattern updates.
• Input: The current pattern index and the rank position of the incoming price data.
• Process: Routes the request to the specific transition table for the chosen order (d=2 to d=5).
• Output: The integer index of the next ordinal pattern.
💮 Table Access: get_table()
This function returns the entire flattened transition table for a specified dimension. This enables local caching of the table (e.g. in an indicator's init() method), avoiding the overhead of repeated library calls during the calculation loop.
💮 Supported Orders & Terminology
The parameter d is the order of ordinal patterns (following Bandt & Pompe 2002). Each pattern of order d contains (d+1) data points, yielding (d+1)! unique patterns:
• d=2: 3 points → 6 unique patterns, 3 successor positions
• d=3: 4 points → 24 unique patterns, 4 successor positions
• d=4: 5 points → 120 unique patterns, 5 successor positions
• d=5: 6 points → 720 unique patterns, 6 successor positions
Note: d=6 is not implemented. The resulting code size (approx. 191k tokens) exceeds the Pine Script limit of 100k tokens (as of 2025-12). Library
[GYTS-CE] Market Regime Detector🧊 Market Regime Detector (Community Edition)
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What is the Market Regime Detector?
The Market Regime Detector is an advanced, consensus-based indicator that identifies the current market state to increase the probability of profitable trades. By distinguishing between trending (bullish or bearish) and cyclic (range-bound) market conditions, this detector helps you select appropriate tactics for different environments. Instead of forcing a single strategy across all market conditions, our detector allows you to adapt your approach based on real-time market behaviour.
💮 The Importance of Market Regimes
Markets constantly shift between different behavioural states or "regimes":
• Bullish trending markets - characterised by sustained upward price movement
• Bearish trending markets - characterised by sustained downward price movement
• Cyclic markets - characterised by range-bound, oscillating behaviour
Each regime requires fundamentally different trading approaches. Trend-following strategies excel in trending markets but fail in cyclic ones, while mean-reversion strategies shine in cyclic markets but underperform in trending conditions. Detecting these regimes is essential for successful trading, which is why we've developed the Market Regime Detector to accurately identify market states using complementary detection methods.
🌸 --------- KEY FEATURES --------- 🌸
💮 Consensus-Based Detection
Rather than relying on a single method, our detector employs two complementary detection methodologies that analyse different aspects of market behaviour:
• Dominant Cycle Average (DCA) - analyzes price movement relative to its lookback period, a proxy for the dominant cycle
• Volatility Channel - examines price behaviour within adaptive volatility bands
These diverse perspectives are synthesised into a robust consensus that minimises false signals while maintaining responsiveness to genuine regime changes.
💮 Dominant Cycle Framework
The Market Regime Detector uses the concept of dominant cycles to establish a reference framework. You can input the dominant cycle period that best represents the natural rhythm of your market, providing a stable foundation for regime detection across different timeframes.
💮 Intuitive Parameter System
We've distilled complex technical parameters into intuitive controls that traders can easily understand:
• Adaptability - how quickly the detector responds to changing market conditions
• Sensitivity - how readily the detector identifies transitions between regimes
• Consensus requirement - how much agreement is needed among detection methods
This approach makes the detector accessible to traders of all experience levels while preserving the power of the underlying algorithms.
💮 Visual Market Feedback
The detector provides clear visual feedback about the current market regime through:
• Colour-coded chart backgrounds (purple shades for bullish, pink for bearish, yellow for cyclic)
• Colour-coded price bars
• Strength indicators showing the degree of consensus
• Customizable colour schemes to match your preferences or trading system
💮 Integration in the GYTS suite
The Market Regime Detector is compatible with the GYTS Suite , i.e. it passes the regime into the 🎼 Order Orchestrator where you can set how to trade the trending and cyclic regime.
🌸 --------- CONFIGURATION SETTINGS --------- 🌸
💮 Adaptability
Controls how quickly the Market Regime detector adapts to changing market conditions. You can see it as a low-frequency, long-term change parameter:
Very Low: Very slow adaptation, most stable but may miss regime changes
Low: Slower adaptation, more stability but less responsiveness
Normal: Balanced between stability and responsiveness
High: Faster adaptation, more responsive but less stable
Very High: Very fast adaptation, highly responsive but may generate false signals
This setting affects lookback periods and filter parameters across all detection methods.
💮 Sensitivity
Controls how sensitive the detector is to market regime transitions. This acts as a high-frequency, short-term change parameter:
Very Low: Requires substantial evidence to identify a regime change
Low: Less sensitive, reduces false signals but may miss some transitions
Normal: Balanced sensitivity suitable for most markets
High: More sensitive, detects subtle regime changes but may have more noise
Very High: Very sensitive, detects minor fluctuations but may produce frequent changes
This setting affects thresholds for regime detection across all methods.
💮 Dominant Cycle Period
This parameter allows you to specify the market's natural rhythm in bars. This represents a complete market cycle (up and down movement). Finding the right value for your specific market and timeframe might require some experimentation, but it's a crucial parameter that helps the detector accurately identify regime changes. Most of the times the cycle is between 20 and 40 bars.
💮 Consensus Mode
Determines how the signals from both detection methods are combined to produce the final market regime:
• Any Method (OR) : Signals bullish/bearish if either method detects that regime. If methods conflict (one bullish, one bearish), the stronger signal wins. More sensitive, catches more regime changes but may produce more false signals.
• All Methods (AND) : Signals only when both methods agree on the regime. More conservative, reduces false signals but might miss some legitimate regime changes.
• Weighted Decision : Balances both methods with equal weighting. Provides a middle ground between sensitivity and stability.
Each mode also calculates a continuous regime strength value that's used for colour intensity in the 'unconstrained' display mode.
💮 Display Mode
Choose how to display the market regime colours:
• Unconstrained regime: Shows the regime strength as a continuous gradient. This provides more nuanced visualisation where the intensity of the colour indicates the strength of the trend.
• Consensus only: Shows only the final consensus regime with fixed colours based on the detected regime type.
The background and bar colours will change to indicate the current market regime:
• Purple shades: Bullish trending market (darker purple indicates stronger bullish trend)
• Pink shades: Bearish trending market (darker pink indicates stronger bearish trend)
• Yellow: Cyclic (range-bound) market
💮 Custom Colour Options
The Market Regime Detector allows you to customize the colour scheme to match your personal preferences or to coordinate with other indicators:
• Use custom colours: Toggle to enable your own colour choices instead of the default scheme
• Transparency: Adjust the transparency level of all regime colours
• Bullish colours: Define custom colours for strong, medium, weak, and very weak bullish trends
• Bearish colours: Define custom colours for strong, medium, weak, and very weak bearish trends
• Cyclic colour: Define a custom colour for cyclic (range-bound) market conditions
🌸 --------- DETECTION METHODS --------- 🌸
💮 Dominant Cycle Average (DCA)
The Dominant Cycle Average method forms a key part of our detection system:
1. Theoretical Foundation :
The DCA method builds on cycle analysis and the observation that in trending markets, price consistently remains on one side of a moving average calculated using the dominant cycle period. In contrast, during cyclic markets, price oscillates around this average.
2. Calculation Process :
• We calculate a Simple Moving Average (SMA) using the specified lookback period - a proxy for the dominant cycle period
• We then analyse the proportion of time that price spends above or below this SMA over a lookback window. The theory is that the price should cross the SMA each half cycle, assuming that the dominant cycle period is correct and price follows a sinusoid.
• This lookback window is adaptive, scaling with the dominant cycle period (controlled by the Adaptability setting)
• The different values are standardised and normalised to possess more resolving power and to be more robust to noise.
3. Regime Classification :
• When the normalised proportion exceeds a positive threshold (determined by Sensitivity setting), the market is classified as bullish trending
• When it falls below a negative threshold, the market is classified as bearish trending
• When the proportion remains between these thresholds, the market is classified as cyclic
💮 Volatility Channel
The Volatility Channel method complements the DCA method by focusing on price movement relative to adaptive volatility bands:
1. Theoretical Foundation :
This method is based on the observation that trending markets tend to sustain movement outside of normal volatility ranges, while cyclic markets tend to remain contained within these ranges. By creating adaptive bands that adjust to current market volatility, we can detect when price behaviour indicates a trending or cyclic regime.
2. Calculation Process :
• We first calculate a smooth base channel center using a low pass filter, creating a noise-reduced centreline for price
• True Range (TR) is used to measure market volatility, which is then smoothed and scaled by the deviation factor (controlled by Sensitivity)
• Upper and lower bands are created by adding and subtracting this scaled volatility from the centreline
• Price is smoothed using an adaptive A2RMA filter, which has a very flat and stable behaviour, to reduce noise while preserving trend characteristics
• The position of this smoothed price relative to the bands is continuously monitored
3. Regime Classification :
• When smoothed price moves above the upper band, the market is classified as bullish trending
• When smoothed price moves below the lower band, the market is classified as bearish trending
• When price remains between the bands, the market is classified as cyclic
• The magnitude of price's excursion beyond the bands is used to determine trend strength
4. Adaptive Behaviour :
• The smoothing periods and deviation calculations automatically adjust based on the Adaptability setting
• The measured volatility is calculated over a period proportional to the dominant cycle, ensuring the detector works across different timeframes
• Both the center line and the bands adapt dynamically to changing market conditions, making the detector responsive yet stable
This method provides a unique perspective that complements the DCA approach, with the consensus mechanism synthesising insights from both methods.
🌸 --------- USAGE GUIDE --------- 🌸
💮 Starting with Default Settings
The default settings (Normal for Adaptability and Sensitivity, Weighted Decision for Consensus Mode) provide a balanced starting point suitable for most markets and timeframes. Begin by observing how these settings identify regimes in your preferred instruments.
💮 Finding the Optimal Dominant Cycle
The dominant cycle period is a critical parameter. Here are some approaches to finding an appropriate value:
• Start with typical values, usually something around 25 works well
• Visually identify the average distance between significant peaks and troughs
• Experiment with different values and observe which provides the most stable regime identification
• Consider using cycle-finding indicators to help identify the natural rhythm of your market
💮 Adjusting Parameters
• If you notice too many regime changes → Decrease Sensitivity or increase Consensus requirement
• If regime changes seem delayed → Increase Adaptability
• If a trending regime is not detected, the market is automatically assigned to be in a cyclic state
• If you want to see more nuanced regime transitions → Try the "unconstrained" display mode (note that this will not affect the output to other indicators)
💮 Trading Applications
Regime-Specific Strategies:
• Bullish Trending Regime - Use trend-following strategies, trail stops wider, focus on breakouts, consider holding positions longer, and emphasize buying dips
• Bearish Trending Regime - Consider shorts, tighter stops, focus on breakdown points, sell rallies, implement downside protection, and reduce position sizes
• Cyclic Regime - Apply mean-reversion strategies, trade range boundaries, apply oscillators, target definable support/resistance levels, and use profit-taking at extremes
Strategy Switching:
Create a set of rules for each market regime and switch between them based on the detector's signal. This approach can significantly improve performance compared to applying a single strategy across all market conditions.
GYTS Suite Integration:
• In the GYTS 🎼 Order Orchestrator, select the '🔗 STREAM-int 🧊 Market Regime' as the market regime source
• Note that the consensus output (i.e. not the "unconstrained" display) will be used in this stream
• Create different strategies for trending (bullish/bearish) and cyclic regimes. The GYTS 🎼 Order Orchestrator is specifically made for this.
• The output stream is actually very simple, and can possibly be used in indicators and strategies as well. It outputs 1 for bullish, -1 for bearish and 0 for cyclic regime.
🌸 --------- FINAL NOTES --------- 🌸
💮 Development Philosophy
The Market Regime Detector has been developed with several key principles in mind:
1. Robustness - The detection methods have been rigorously tested across diverse markets and timeframes to ensure reliable performance.
2. Adaptability - The detector automatically adjusts to changing market conditions, requiring minimal manual intervention.
3. Complementarity - Each detection method provides a unique perspective, with the collective consensus being more reliable than any individual method.
4. Intuitiveness - Complex technical parameters have been abstracted into easily understood controls.
💮 Ongoing Refinement
The Market Regime Detector is under continuous development. We regularly:
• Fine-tune parameters based on expanded market data
• Research and integrate new detection methodologies
• Optimise computational efficiency for real-time analysis
Your feedback and suggestions are very important in this ongoing refinement process! Indicator
[GYTS] Filters ToolkitFilters Toolkit indicator
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 Overview
The GYTS Filters Toolkit indicator is an advanced, interactive interface built atop the high‐performance, curated functions provided by the FiltersToolkit library . It allows traders to experiment with different combinations of filtering methods -— from smoothing low-pass filters to aggressive detrenders. With this toolkit, you can build custom indicators tailored to your specific trading strategy, whether you're looking for trend following, mean reversion, or cycle identification approaches.
🌸 --------- 2. FILTER METHODS AND TYPES --------- 🌸
💮 Filter categories
The available filters fall into four main categories, each marked with a distinct symbol:
🌗 Low Pass Filters (Smoothers)
These filters attenuate high-frequency components (noise) while allowing low-frequency components (trends) to pass through. Examples include:
Ultimate Smoother
Super Smoother (2-pole and 3-pole variants)
MESA Adaptive Moving Average (MAMA) and Following Adaptive Moving Average (FAMA)
BiQuad Low Pass Filter
ADXvma (Adaptive Directional Volatility Moving Average)
A2RMA (Adaptive Autonomous Recursive Moving Average)
Low pass filters are displayed on the price chart by default, as they follow the overall price movement. If they are combined with a high-pass or bandpass filter, they will be displayed in the subgraph.
🌓 High Pass Filters (Detrenders)
These filters do the opposite of low pass filters - they remove low-frequency components (trends) while allowing high-frequency components to pass through. Examples include:
Butterworth High Pass Filter
BiQuad High Pass Filter
High pass filters are displayed as oscillators in the subgraph below the price chart, as they fluctuate around a zero line.
🌑 Band Pass Filters (Cycle Isolators)
These filters combine aspects of both low and high pass filters, isolating specific frequency ranges while attenuating both higher and lower frequencies. Examples include:
Ehlers Bandpass Filter
Cyber Cycle
Relative Vigor Index (RVI)
BiQuad Bandpass Filter
Band pass filters are also displayed as oscillators in a separate panel.
🔮 Predictive Filter
Voss Predictive Filter: A special filter that attempts to predict future values of band-limited signals (only to be used as post-filter). Keep its prediction horizon short (1–3 bars) for reasonable accuracy.
Note that the the library contains elaborate documentation and source material of each filter.
🌸 --------- 3. INDICATOR FEATURES --------- 🌸
💮 Multi-filter configuration
One of the most powerful aspects of this indicator is the ability to configure multiple filters. compare them and observe their combined effects. There are four primary filters, each with its own parameter settings.
💮 Post-filtering
Process a filter’s output through an additional filter by enabling the post-filter option. This creates a filter chain where the output of one filter becomes the input to another. Some powerful combinations include:
Ultimate Smoother → MAMA: Creates an adaptive smoothing effect that responds well to market changes, good for trend-following strategies
Butterworth → Super Smoother → Butterworth: Produces a well-behaved oscillator with minimal phase distortion, John Ehlers also calls a "roofing filter". Great for identifying overbought/oversold conditions with minimal lag.
A bandpass filter → Voss Prediction filter: Attempts to predict future movements of cyclical components, handy to find peaks and troughs of the market cycle.
💮 Aggregate filters
Arguably the coolest feature: aggregating filters allow you to combine multiple filters with different weights. Important notes about aggregation:
You can only aggregate filters that appear on the same chart (price chart or oscillator panel).
The weights are automatically normalised, so only their relative values matter
Setting a weight to 0 (zero) excludes that filter from the aggregation
Filters don't need to be visibly displayed to be included in aggregation
💮 Rich visualisation & alerts
The indicator intelligently determines whether a filter is displayed on the price chart or in the subgraph (as an oscillator) based on its characteristics.
Dynamic colour palettes, adjustable line widths, transparency, and custom fill between any of enabled filters or between oscillators and the zero-line.
A clear legend showing which filters are active and how they're configured
Alerts for direction changes and crossovers of all filters
🌸 --------- 4. ACKNOWLEDGEMENTS --------- 🌸
This toolkit builds on the work of numerous pioneers in technical analysis and digital signal processing:
John Ehlers, whose groundbreaking research forms the foundation of many filters.
Robert Bristow-Johnson for the BiQuad filter formulations.
The PulseWire community, especially @The_Peaceful_Lizard, @alexgrover, and others mentioned in the code of the library.
Everyone who has provided feedback, testing and support!
Indicator
[GYTS] FiltersToolkit LibraryFiltersToolkit Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 What Does This Library Contain?
This library is a curated collection of high-performance digital signal processing (DSP) filters and auxiliary functions designed specifically for financial time series analysis. It includes a shortlist of our favourite and best performing filters — each rigorously tested and selected for their responsiveness, minimal lag and robustness in diverse market conditions. These tools form an integral part of the GoemonYae Trading System (GYTS), chosen for their unique characteristics in handling market data.
The library contains two main categories:
1. Smoothing filters (low-pass filters and moving averages) for e.g. denoising, trend following
2. Detrending tools (high-pass and band-pass filters, known as "oscillators") for e.g. mean reversion
This collection is finely tuned for practical trading applications and is therefore not meant to be exhaustive. However, will continue to expand as we discover and validate new filtering techniques. I welcome collaboration and suggestions for novel approaches.
🌸 ——— 2. ADDED VALUE ——— 🌸
💮 Unified syntax and comprehensive documentation
The FiltersToolkit Library brings together a wide array of valuable filters under a unified, intuitive syntax. Each function is thoroughly documented, with clear explanations and academic sources that underline the mathematical rigour behind the methods. This level of documentation not only facilitates integration into trading strategies but also helps underlying the underlying concepts and rationale.
💮 Optimised performance and readability
The code prioritizes computational efficiency while maintaining readability. Key optimizations include:
- Minimizing redundant calculations in recursive filters
- Smart coefficient caching
- Efficient state management
- Vectorized operations where applicable
💮 Enhanced functionality and flexibility
Some filters in this library introduce extended functionality beyond the original publications. For instance, the MESA Adaptive Moving Average (MAMA) and Ehlers’ Combined Bandpass Filter incorporate multiple variations found in the literature, thereby providing traders with flexible tools that can be fine-tuned to different market conditions.
🌸 ——— 3. THE FILTERS ——— 🌸
💮 Hilbert Transform Function
This function implements the Hilbert Transform as utilised by John Ehlers. It converts a real-valued time series into its analytic signal, enabling the extraction of instantaneous phase and frequency information—an essential step in adaptive filtering.
Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004)
💮 Homodyne Discriminator
By leveraging the Hilbert Transform, this function computes the dominant cycle period through a Homodyne Discriminator. It extracts the in-phase and quadrature components of the signal, facilitating a robust estimation of the underlying cycle characteristics.
Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004)
💮 MESA Adaptive Moving Average (MAMA)
An advanced dual-stage adaptive moving average, this function outputs both the MAMA and its companion FAMA. It combines adaptive alpha computation with elements from Kaufman’s Adaptive Moving Average (KAMA) to provide a responsive and reliable trend indicator.
Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004)
💮 BiQuad Filters
A family of second-order recursive filters offering exceptional control over frequency response:
- High-pass filter for detrending
- Low-pass filter for smooth trend following
- Band-pass filter for cycle isolation
The quality factor (Q) parameter allows fine-tuning of the resonance characteristics, making these filters highly adaptable to different market conditions.
Source: Robert Bristow-Johnson's Audio EQ Cookbook, implemented by @The_Peaceful_Lizard
💮 Relative Vigor Index (RVI)
This filter evaluates the strength of a trend by comparing the closing price to the trading range. Operating similarly to a band-pass filter, the RVI provides insights into market momentum and potential reversals.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 Cyber Cycle
The Cyber Cycle filter emphasises market cycles by smoothing out noise and highlighting the dominant cyclical behaviour. It is particularly useful for detecting trend reversals and cyclical patterns in the price data.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 Butterworth High Pass Filter
Inspired by the classical Butterworth design, this filter achieves a maximally flat magnitude response in the passband while effectively removing low-frequency trends. Its design minimises phase distortion, which is vital for accurate signal interpretation.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 2-Pole SuperSmoother
Employing a two-pole design, the SuperSmoother filter reduces high-frequency noise with minimal lag. It is engineered to preserve trend integrity while offering a smooth output even in noisy market conditions.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 3-Pole SuperSmoother
An extension of the 2-pole design, the 3-pole SuperSmoother further attenuates high-frequency noise. Its additional pole delivers enhanced smoothing at the cost of slightly increased lag.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 Adaptive Directional Volatility Moving Average (ADXVma)
This adaptive moving average adjusts its smoothing factor based on directional volatility. By combining true range and directional movement measurements, it remains exceptionally flat during ranging markets and responsive during directional moves.
Source: Various implementations across platforms, unified and optimized
💮 Ehlers Combined Bandpass Filter with Automated Gain Control (AGC)
This sophisticated filter merges a highpass pre-processing stage with a bandpass filter. An integrated Automated Gain Control normalises the output to a consistent range, while offering both regular and truncated recursive formulations to manage lag.
Source: John F. Ehlers – “Truncated Indicators” (2020), “Cycle Analytics for Traders” (2013)
💮 Voss Predictive Filter
A forward-looking filter that predicts future values of a band-limited signal in real time. By utilising multiple time-delayed feedback terms, it provides anticipatory coupling and delivers a short-term predictive signal.
Source: John Ehlers - "A Peek Into The Future" (TASC 2019-08)
💮 Adaptive Autonomous Recursive Moving Average (A2RMA)
This filter dynamically adjusts its smoothing through an adaptive mechanism based on an efficiency ratio and a dynamic threshold. A double application of an adaptive moving average ensures both responsiveness and stability in volatile and ranging markets alike. Very flat response when properly tuned.
Source: @alexgrover (2019)
💮 Ultimate Smoother (2-Pole)
The Ultimate Smoother filter is engineered to achieve near-zero lag in its passband by subtracting a high-pass response from an all-pass response. This creates a filter that maintains signal fidelity at low frequencies while effectively filtering higher frequencies at the expense of slight overshooting.
Source: John Ehlers - TASC 2024-04 "The Ultimate Smoother"
Note: This library is actively maintained and enhanced. Suggestions for additional filters or improvements are welcome through the usual channels. The source code contains a list of tested filters that did not make it into the curated collection. Library
ColourUtilitiesLibrary "ColourUtilities"
Utility functions for colour manipulation
adjust_colour(rgb, desaturation_amount, transparency_amount)
to reduce saturation or increase transparency of an RGB colour
Parameters:
rgb (color)
desaturation_amount (float) : 0 means no desaturation (colours remains as-is), and 1 means full desaturation (colour turns grey). Can also be used inversely with negative numbers
transparency_amount (float) : How much more transparent the default transparency should become. E.g. with a value of 0.5, a transparency of 0 becomes 50 and 40 becomes 70. A value of 1 makes it fully transparent, en -1 fully opaque.
Returns: color with adjusted saturation and transparency
method apply_default_palette(self, palette_name)
Some nice looking colour palettes, consisting of 6 gradient colours, are already defined here and can be quickly applied to the Palette class
Namespace types: Palette
Parameters:
self (Palette)
palette_name (string) : Currently there are 4 6-coloured palettes available: "GYTS flux signal", "GYTS purple", "GYTS flux filter" and "GYTS maroon"
Returns: None, as it populates the Palette class with pre-defined colours
method get_colour(self, colour_no, transparency)
Retrieves colour from the palette and possibly changes transparency if set
Namespace types: Palette
Parameters:
self (Palette)
colour_no (int) : from the palette
transparency (int) : to possibly change the default transparency of the palette
Returns: colour
method get_dynamic_colour(self, x, mid_point, colour_lb, colour_ub, trend_lookback, use_rate)
Retrieves a colour based on strength and direction of the passed series
Namespace types: Palette
Parameters:
self (Palette)
x (float) : the input data series
mid_point (float) : value as a cutoff point where the bullish/bearish colour scenario
colour_lb (float) : value (lower bound) where to apply the bearish colour at full strength
colour_ub (float) : value (upper bound) where to apply the bullish colour at full strength
trend_lookback (int) : how much bars back to check if there was a consistent move into a certain direction, otherwise a the neutral colour from the centre of the palette will be used.
use_rate (bool) : whether to use the rate (proportional difference with previous `x` value) or the input series `x` directly
Returns: colour
Palette
Fields:
transparency (series__integer)
palette (array__color) Library
