True Time Price Profile - Hybrid Dynamic Bins[ALT_analyst]True Time Price Profile - Hybrid Dynamic Bins
◆ NOTICE / DISCLAIMER
This architecture is NOT a standard Volume Profile (VP) or a conventional Time Price Opportunity (TPO) indicator.
It is a highly advanced, multi-variable structural density engine.
It was specifically designed to mathematically extract institutional defense lines and localized price absorption in environments lacking reliable tick volume (e.g., Forex, CFD, Indices),
functioning as a rigorous technical benchmark for supply/demand extraction.
◆ EXECUTIVE SUMMARY
This script is deployed as a Proof of Concept (PoC) to demonstrate the integration of price absorption, time-based variance,
and strict pro-rata energy distribution within a localized UI rendering environment.
By discarding standard aggregation methods, this open-source architecture isolates the true "quality" of price stagnation,
exposing anomalous market states where large capital defends specific price buckets.
◆ ARCHITECTURE & QUANTITATIVE LOGIC
Standard profiles often struggle because they cannot distinguish between a "rapid vacuum passing" and a "defended consolidation."
This engine utilizes three proprietary layers to resolve this logic gap:
Pro-Rata Energy Distribution Engine
To prevent large-range bars (e.g., sudden momentum spikes) from artificially inflating the profile score across empty price vacuums, this script enforces a strict pro-rata allocation matrix.
Let N_bins be the total number of price bins a single bar intersects.
The assigned value for each specific bin is calculated as:
Apportioned Value = Base Value / N_bins
This completely neutralizes vacuum zones, correctly assigning mass only to true areas of conflict.
Velocity & Acceleration (Absorption) Evaluator
Instead of counting volume, the script measures the deceleration of price action.
It compares the high-low range of the current bar (v_curr) against the previous bar (v_prev). A negative acceleration (accel < 0) indicates kinetic energy is being absorbed by limit orders.
This absolute delta is extracted as the base absorption value (|a|).
Time Variance Logic (Market Memory)
A price level tested multiple times over a prolonged period holds significantly more structural integrity than a level tested only once.
The engine applies the statistical variance of the normalized time index (t) to scale the localized importance of a bin:
Variance (σ²) = (Sum of t² / n) - (Average t)²
The final Hybrid Score is the integration of absorbed energy scaled by the logarithmic variance:
Score = Sum( |a| * ln(1 + σ²) )
◆ PRACTICAL APPLICATION: HOW TO TRADE WITH THIS ENGINE
Instead of blindly treating every high-volume node as support/resistance, utilize this engine to identify Structural Friction:
Locating Hidden Institutional Limits:
Bins with exceptionally high Hybrid Scores often act as heavy liquidity pools.
Price action will typically stall or reverse sharply upon re-entering these zones.
Breakout Validation:
If price breaks out of a Value Area (VA) without generating new high-score bins, it indicates a lack of limit-order resistance (a vacuum).
These moves are prone to rapid continuation or swift mean-reversion sweeps.
Cross-Session Node Alignment (Breakout Threshold):
By anchoring the profile to short, sequential sessions, observe if high-scoring nodes (POCs) align horizontally at the same price level across multiple independent profiles.
This structural anomaly signifies a massive, sustained accumulation of limit orders.
A decisive price breach of this specific alignment typically triggers a high-probability volatility breakout, as the defended liquidity pool is rapidly consumed.
◆ SYSTEM CAPABILITIES AND LIMITATIONS
Visual Synthesis of Invisible Nodes:
Resolves precise support/resistance vectors purely from price action kinetics, independent of broker volume feeds.
Dynamic Resolution Scaling:
The bin size is strictly tethered to the Average True Range (ATR), ensuring the profile grid automatically calibrates to the underlying asset's volatility regime.
Limitations & Warnings:
PulseWire enforces a strict cap of 500 max boxes/lines per indicator. To prevent script execution limits or array errors, the maximum lookback and bin count are dynamically capped.
Furthermore, if the scaled ATR drops to absolute zero, the geometric grid cannot initialize.
◆ INPUT PARAMETERS REFERENCE
Live Update Frequency:
Toggle between 'Update on Every Tick' and 'Update on Bar Close'.
CRITICAL WARNING: Using tick updates combined with multiple MTF arrays on a fast timeframe will cause localized UI lag. Use 'Bar Close' as a CPU saver.
Profile Calculation Mode:
Select 'Classic' for standard aggregation, or 'Hybrid' to engage the Absorption + Variance matrix (The core edge of this tool).
Grid Step Multiplier:
Lower values increase vertical resolution.
Warning: Values below 0.05 on high-volatility assets may trigger the 500-box rendering limit.
Show Debug Data Table:
Projects a live array matrix on the bottom right, displaying precise Price, Count, Absorption, Variance, and Hybrid Scores for absolute algorithmic transparency.
Indicator
Anchored VWAP Reversion ChannelAnchored VWAP Reversion Channel — Regime-Gated Fade Framework
## What this script does
This is an **analytical study** that frames mean-reversion ("fade") setups around an **anchored, volume-weighted regression channel**, then **gates** those setups by a statistical market-state test and **scores** them against their own forward outcomes. It does not place orders and it is not a signal service — its purpose is to let you see, on your own instrument and timeframe, whether fading a stretched move actually has an edge, instead of assuming it does.
It plots one channel (a centre line plus inner/outer residual-σ bands), marks fade setups at the outer band, draws supporting context (volume-profile POC / value area, untested prior-session POCs, momentum divergences, liquidity sweeps, and multi-timeframe trend lines), and reports a compact validation panel.
## Why these components are combined (mashup rationale)
Fading an extreme is really three separate questions, and no single classic indicator answers all three. Stacking look-alike indicators just echoes one input, so this tool deliberately combines **three non-redundant lenses and makes them check each other**:
1. **WHERE is price stretched?** — A **volume-weighted polynomial regression** anchored at the most recent swing pivot, with **residual-σ bands**. Because the curve tilts with the active leg, an outer-band tag stays meaningful even inside a trend, where a flat cumulative VWAP would not. A **volume profile** anchored to the *same* window supplies POC and value area, and prior-session POCs that have never since been traded through become **reversion targets**.
2. **Is a reversion actually firing here?** — Three orthogonal **tells** evaluated only at the band: a **close-back rejection**, a **band-confluent momentum divergence**, and an **equal-high/low liquidity sweep** (stop-run). Crucially, all three are derived from the same stretch, so their agreement is shrunk by a **design-effect correction** (effective-sample-size): three correlated echoes are not allowed to masquerade as three independent confirmations.
3. **Is the market in a reverting state at all?** — A **regime gate** combining a **variance-ratio test** and a **reversion-trust correlation** only lets a fade through when recent increments are offsetting (mean-reverting) rather than compounding (trending).
The pieces are not bolted together side by side: they share **one geometry** (the anchored channel) and **one volatility unit** (residual σ / ATR), and each can veto the others. A band tag with no tell does nothing; a tell with no reverting regime does nothing. The design goal is to **suppress** low-quality fades — into a trend, mid-range, or backed by a single echoed tell — more than to generate them.
## The honesty layer (what makes this more than a drawing)
Every fade that fires is logged and, a fixed horizon later, **resolved**: its forward return is measured in ATR units and tabulated **with the regime gate ON versus OFF**, reporting follow-through %, whipsaw %, a Wilson 95% confidence interval, and the **mean return per fade**. A per-fade series also exports to the Data Window so you can study the full return distribution offline. The gate has to **beat its own ungated baseline** to justify itself — the framework is built to be tested, not trusted blindly.
## How to use it
1. Set the **Price source** (group 01). It works on any symbol and any market; volume-based parts need a real volume feed.
2. A fade **arms** when price tags the outer band **and** at least one tell prints, then **passes** only if the regime gate reports a reverting state. Solid triangles are gated fades; the target is the centre line or the nearest untested POC.
3. Read the panel top-down: does **Gate ON** beat **Gate OFF** on both follow-through and mean R, with non-overlapping intervals and a reasonable sample size? If not, the edge is not present on this symbol/timeframe — change them rather than forcing the trade.
4. The signal lives on **higher intraday timeframes**; one-minute data is mostly noise.
## Defaults
Shipped tuned for **NSE:NIFTY** index futures on intraday timeframes (sources, pivot lengths, value-area %, and the Tuesday-style weekly session context reflect that instrument). Every value is exposed as an input — change the **Price source** and the relevant lengths to run the framework on any other instrument or market.
## What is original
The original work is the **coordination**, not any single formula: an anchored polynomial-regression channel used as a reversion frame, three decorrelated band tells fused by a design-effect shrink, a statistical regime gate, and a built-in A/B + forward-return validation harness — combined so each lens can veto the others and the whole thing reports its own hit rate. It is not a re-skin of one indicator.
## Concept credits (techniques are standard; this implementation is original)
Anchored VWAP (standard); volume-weighted least-squares / polynomial regression (standard); residual-σ channel (standard); Volume Profile, Value Area and POC — Market Profile, Steidlmayer / CBOT; Variance-Ratio test — Lo & MacKinlay (1988); design effect / effective sample size — Kish (1965); proportion confidence interval — Wilson (1927); ATR trailing stop / Supertrend (classic, used for the multi-timeframe context lines); RSI — Wilder; Stochastic — Lane.
## Disclaimer
For research and education only. This is an analytical study, **not** financial advice, **not** a recommendation, and **not** a guarantee of future results. All statistics shown are **in-sample** on loaded history, close-to-close, without costs or slippage — a study aid, not a backtest. Mean reversion fails in trends and through regime breaks. Do your own research and manage your own risk.
Indicator
Volatility Pressure & Regime AnalyzerVolatility Pressure & Regime Analyzer
## What this script does
VPRA estimates **when a market is loading energy for an outsized move, how large that move could be, and whether the current regime favors chasing or fading the breakout**. It condenses this into one on-chart verdict panel, directional signal markers, a regime ribbon, and a forecast of the expected move in ATR and points.
It works on **any symbol, any market, any timeframe**. A related volatility index and a companion symbol (the underlying if you chart a derivative, or vice versa) are optional inputs that sharpen the analysis; both can be disabled and the model renormalizes to price-only mode automatically.
## Why these components are combined (mashup justification)
Each module answers a question the others cannot, and the signal only fires when their answers agree. None of them is a stock indicator pasted alongside another — they are inputs to a single pressure model:
1. **Compression (ATR percentile)** answers *"is energy being stored?"* Quiet ranges precede expansion, but compression alone says nothing about direction or timing.
2. **Implied-vs-realized volatility dislocation** (optional vol index) answers *"is the options market mispricing the calm?"* A large gap between implied and realized volatility marks complacency or stress that compression alone cannot see.
3. **Basis tension** (optional companion symbol) answers *"is positioning leaning?"* Momentum in the derivative-to-underlying spread, and outright backwardation, reveal funding pressure and de-risking invisible in a single price series.
4. **Convexity and trend inefficiency** (return acceleration, efficiency ratio) answer *"is price behavior becoming unstable?"*
These four are blended into one **Pressure score (0–100)**, percent-ranked against its own history so thresholds adapt to every symbol and timeframe.
5. **A variance-ratio regime filter** answers *"will the break run or get faded?"* The ratio of k-bar to 1-bar return variance classifies the tape as mean-reverting (pinning) or trending (amplifying). Breakouts in a pinning regime are statistically more likely to fail, so the script can label or skip them.
6. **A multi-timeframe trend filter (Ichimoku cloud bias on the chart TF + three higher TFs)** answers *"is the release direction supported by structure?"* It grades signals rather than generating them. Higher-timeframe values are taken from **closed bars by default, so the confluence grade does not repaint**.
7. **Session, expiry, gap and event context** scale the expected-move forecast: an expiry-afternoon release during a volatility spike forecasts a larger move than a sleepy mid-session one.
Removing any module degrades a specific, named capability — that is the test the combination was built to pass.
## How a signal is generated
A marker prints only when **all** of the following align: pressure has reached a high percentile of its own history within a short lookback ("loaded"), the current bar shows a genuine range expansion ("release"), the condition persists for a confirmation bar count, a debounce gap has passed, and (optionally) the regime and trend filters pass. Direction is scored from **trigger-break** (close beyond the prior N-bar extreme), **close location** within the bar, and short momentum.
Marker color encodes the inferred event type: expiry-session releases, volatility-co-movement squeezes (price and vol index moving together — a short-covering tell), or plain expansions. The glow ring encodes how many higher timeframes agree. An ⓘ label stores a full diagnostic snapshot (pressure, regime, instability, basis, energy, session, expected move) in its tooltip for every signal.
## How to use it
- Apply to a liquid symbol; set "This chart is" to Derivative or Underlying, point the companion and volatility-index inputs at your market's related symbols (or disable them), and set your session hours and expiry weekday.
- Read the panel top-down: **Regime** (chase vs fade), **Pressure/Energy** (how loaded), **Move size** (forecast), **Trend align / HTF** (structure), **Triggers** (the price levels that confirm).
- Use the "Filter" modes to suppress signals against regime or higher-timeframe structure, or leave them as badges and judge manually.
- The advanced rows show per-type follow-through statistics (hit rate, average favorable and adverse excursion in ATR) and an early-vs-late history split as a coarse robustness check. **These are in-sample descriptive statistics, not a backtest.** A companion strategy script with identical logic is available for proper backtesting with costs.
- Alerts: per-signal dynamic alert with all values (webhook-ready), plus static conditions for expiry signals, releases, critical pressure, and vol shocks.
## Originality
The pressure blend (compression x vol-dislocation x basis tension x convexity x inefficiency, percent-rank normalized), the variance-ratio regime gate applied to breakout qualification, the compression-energy budget, and the per-type MFE/MAE statistics with an early/late split are original constructions written from first principles for this script. The only classical components used are public-domain building blocks (ATR, Bollinger/Keltner-style compression logic via ATR percentile, Ichimoku cloud bias as a trend filter, Kaufman efficiency ratio), each justified above.
## Limitations (please read)
- Dealer-positioning effects (often discussed as gamma/vanna/charm) are **inferred from price, volatility and basis behavior**. This script does not and cannot read option-chain open interest. Labels such as "gamma blast" describe an expiry-session release pattern, not a measured dealer position.
- All on-panel statistics are computed on the loaded chart history and will differ across symbols, timeframes and history length.
- Higher-timeframe confluence uses closed HTF bars by default (no repaint); the current chart bar still forms in real time, as with any script.
- Expected-move figures are model estimates, not guarantees.
This script is for education and analysis. It is **not financial advice**; trade at your own risk and test before use.
Indicator
Statistical Mean-Reversion Engine [SMRE]## Statistical Mean-Reversion Engine (SMRE)
SMRE is an open-source mean-reversion indicator that combines a rigorous statistical core with up to eight optional confirmation layers, designed primarily for index-futures trading on intraday timeframes (1-minute through 1-hour).
### What it does
For every bar, SMRE fits an Ornstein-Uhlenbeck (OU) process to the recent price series via linear regression on lag-1 prices, yielding four outputs:
- **μ (the mean)** — the equilibrium price the series is reverting to
- **θ (mean-reversion speed)** — how strongly the series pulls back to μ
- **HL (half-life)** — how many bars it takes to revert halfway
- **σ_eq (stationary residual variance)** — used to z-score the current price
The current price's z-score against μ (the "OU Z") is the primary signal. When |OU Z| exceeds a configurable threshold, a mean-reversion entry is considered — but only after the script also confirms that the recent price series is genuinely stationary using three orthogonal statistical tests:
- **Hurst exponent** must be below 0.55 (i.e., the series is not persistently trending)
- **Augmented Dickey-Fuller** t-statistic must be below -2.86 (rejects unit root)
- **Variance Ratio** test at q=4 must be below 1.0 (variance grows sub-linearly with horizon)
If all four conditions pass, the L1 (statistical core) signal fires.
### Why the multi-layer structure (mashup justification)
A single OU-based mean-reversion signal works well in stationary regimes but degrades in trending or volatile conditions. SMRE addresses this by validating each potential entry through up to eight orthogonal confirmation channels, each measuring something the others do not:
- **L2 — Volatility Regime (6-state):** Classifies market state via VIX, ADX, and realized volatility. Suppresses signals during high-trend conditions (regime 6, "Spike") where mean-reversion historically fails.
- **L3 — Spot-Futures Basis (Kalman filter):** Tracks the deviation between actual and theoretical futures pricing. Statistically significant basis dislocations often resolve via mean-reversion.
- **L4 — Options Surface:** Computes ATM implied volatility from straddle pricing and a skew z-score from OTM put/call ratio. Optional; requires user to provide option symbols.
- **L5 — Microstructure:** Blends rolling VWAP and session-anchored VWAP z-scores with VPIN (a volume-clock toxicity proxy) and order-flow imbalance. Captures flow-based exhaustion.
- **L6 — Gamma Walls (GEX) OR Put-Call Ratio:** Two mutually exclusive options. GEX requires OI symbols at five strikes; PCR requires a single broker-published PCR feed. Both detect option-driven price magnets.
- **L7 — Dispersion:** Rolling correlation of index returns with its top 5 constituent stocks' returns. High dispersion (low correlation) penalizes signals; high cohesion boosts them.
- **L7b — Residual Dispersion:** Idiosyncratic residual z-scores (β-adjusted) per constituent. If 3 of 5 stocks show same-sign extreme residuals, the index is detached from constituents — strong mean-reversion candidate.
- **L9 — Cross-Asset Stress:** Sigma-normalized stress across USD/INR, DXY, and crude oil. Penalizes signals during cross-asset hedging cascades.
Each layer outputs a {direction, strength} pair. The Layer 8 fusion engine combines these via a weighted composite score (default weights: L1=0.28, L5=0.22, L3=0.18, L4=0.12, L6/L7b=0.10), then applies a regime multiplier (L2 × L7 × VRP × cross-asset × expiry), clamped to to prevent extreme compounding.
If the absolute composite score crosses one of three thresholds (0.25 / 0.40 / 0.45 by default), a signal is fired at Scalp / Swing / Session horizon respectively. A TCA cost filter then validates that the expected move (distance to μ) exceeds estimated round-trip transaction cost; otherwise the signal is suppressed.
### Originality
The author is not aware of any other public Pine script that implements the full OU-fit chain (mean, mean-reversion speed, half-life, stationary variance) together with all three stationarity tests (Hurst, ADF, Variance Ratio) directly in Pine v6 — every step is computed natively, no external library calls. Additionally, the session-anchored VWAP with running volume-weighted sigma bands, the rolling-beta residual dispersion across multiple constituents, and the Kalman-filtered futures-basis residual are original Pine implementations. The signal telemetry module (a 200-signal FIFO ring buffer with horizon × composite-magnitude bucket attribution) is also an original diagnostic tool.
### How to use
1. **Apply to an index futures chart.** Defaults are pre-configured for NSE NIFTY1! futures, but inputs allow any index — change the VIX symbol, spot/futures symbols, constituent symbols, and currency pairs.
2. **Read the compact dashboard.** It's a single 9-row table (default position: middle-right) showing only what you need to evaluate a setup:
| Row | What it shows | What it means |
|---|---|---|
| Title | Profile + OU window in use | Confirms which calibration is active |
| OU Z-Score | Z-score with half-life (HL) | How extended price is + how long mean-reversion typically takes |
| Stat Validity | H / ADF / VR pass-fail | Whether the recent series is actually stationary (all 3 must pass) |
| Regime | Volatility state + VIX value | Whether market conditions favor mean-reversion |
| Composite | Fused score × regime multiplier | The unified signal strength |
| Confluence | Layers agreeing (out of 6) | How many orthogonal signals support the direction |
| TCA Edge | Expected move in bps + PASS/FAIL | Whether the trade clears transaction costs |
| E / SL / TP | Entry, Stop, Target + Risk:Reward | The trade levels if a signal fires |
| **DECISION** | Direction · Horizon · Side | The actionable output (green=long, red=short, gray=neutral) |
3. **Trade levels and markers.** When a signal fires, entry/stop/target lines auto-plot on the chart. Stop is ATR-based (default 1.2× ATR); target is min(OU mean μ, entry + 2× ATR). Triangle markers plot below (long) or above (short) the bar — small for Scalp, medium for Swing, large for Session.
4. **Optional diagnostic.** A separate Signal Telemetry table (disabled by default; enable via the "Show Telemetry Dashboard" input) tracks the last 200 signals' outcomes (win = price touched μ, loss = stop hit, expired = timeout) and reports hit rate by horizon × composite-magnitude bucket. This is a backward-looking diagnostic, not a backtest.
### Recommended chart and timeframe
This indicator was developed and parameter-tested primarily on NIFTY1! futures. The OU window auto-mapping (1m→32, 2m→20, 5m→12, 15m→32, 30m→20, 1h→24) was selected empirically through parameter sweeps. Users on other instruments should expect to tune the OU window manually or accept the auto-mapped default as a starting point.
The indicator works on any timeframe between 1 minute and daily, though intraday timeframes (1m through 1h) are where the multi-layer confluence adds the most value.
### Important notes
- This is an **indicator**, not a strategy — no backtest equity curve is produced. The telemetry table is a descriptive measure of recent signal outcomes only.
- Many layers are **optional**. If you don't have symbols for options OI, just leave those inputs blank; the script will redistribute composite weight naturally across the active layers.
- Signals can fluctuate intra-bar before bar close, especially in real-time mode. For consistent behavior, evaluate signals on closed bars only.
- The default constituents (top-5 NIFTY weights) need to be changed in the L7 inputs to use this on a different index.
### Disclaimer
This indicator is published for educational and research purposes only. It is not financial advice, not an investment recommendation, and not a solicitation to trade. Past behavior of signals does not guarantee future results. Trading futures, options, and equities carries substantial risk of loss. You are solely responsible for your trading decisions. The author makes no representations about the accuracy, completeness, or suitability of this indicator for any particular purpose. Use at your own risk, and always consult a qualified financial professional before trading.
Indicator
Indicator
LibWghtLibrary "LibWght"
This is a library of mathematical and statistical functions
designed for quantitative analysis in Pine Script. Its core
principle is the integration of a custom weighting series
(e.g., volume) into a wide array of standard technical
analysis calculations.
Key Capabilities:
1. **Universal Weighting:** All exported functions accept a `weight`
parameter. This allows standard calculations (like moving
averages, RSI, and standard deviation) to be influenced by an
external data series, such as volume or tick count.
2. **Weighted Averages and Indicators:** Includes a comprehensive
collection of weighted functions:
- **Moving Averages:** `wSma`, `wEma`, `wWma`, `wRma` (Wilder's),
`wHma` (Hull), and `wLSma` (Least Squares / Linear Regression).
- **Oscillators & Ranges:** `wRsi`, `wAtr` (Average True Range),
`wTr` (True Range), and `wR` (High-Low Range).
3. **Volatility Decomposition:** Provides functions to decompose
total variance into distinct components for market analysis.
- **Two-Way Decomposition (`wTotVar`):** Separates variance into
**between-bar** (directional) and **within-bar** (noise)
components.
- **Three-Way Decomposition (`wLRTotVar`):** Decomposes variance
relative to a linear regression into **Trend** (explained by
the LR slope), **Residual** (mean-reversion around the
LR line), and **Within-Bar** (noise) components.
- **Local Volatility (`wLRLocTotStdDev`):** Measures the total
"noise" (within-bar + residual) around the trend line.
4. **Weighted Statistics and Regression:** Provides a robust
function for Weighted Linear Regression (`wLinReg`) and a
full suite of related statistical measures:
- **Between-Bar Stats:** `wBtwVar`, `wBtwStdDev`, `wBtwStdErr`.
- **Residual Stats:** `wResVar`, `wResStdDev`, `wResStdErr`.
5. **Fallback Mechanism:** All functions are designed for reliability.
If the total weight over the lookback period is zero (e.g., in
a no-volume period), the algorithms automatically fall back to
their unweighted, uniform-weight equivalents (e.g., `wSma`
becomes a standard `ta.sma`), preventing errors and ensuring
continuous calculation.
---
**DISCLAIMER**
This library is provided "AS IS" and for informational and
educational purposes only. It does not constitute financial,
investment, or trading advice.
The author assumes no liability for any errors, inaccuracies,
or omissions in the code. Using this library to build
trading indicators or strategies is entirely at your own risk.
As a developer using this library, you are solely responsible
for the rigorous testing, validation, and performance of any
scripts you create based on these functions. The author shall
not be held liable for any financial losses incurred directly
or indirectly from the use of this library or any scripts
derived from it.
wSma(source, weight, length)
Weighted Simple Moving Average (linear kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Linear-kernel weighted mean; falls back to
the arithmetic mean if Σweight = 0.
wEma(source, weight, length)
Weighted EMA (exponential kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Exponential-kernel weighted mean; falls
back to classic EMA if Σweight = 0.
wWma(source, weight, length)
Weighted WMA (linear kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Linear-kernel weighted mean; falls back to
classic WMA if Σweight = 0.
wRma(source, weight, length)
Weighted RMA (Wilder kernel, α = 1/len).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Wilder-kernel weighted mean; falls back to
classic RMA if Σweight = 0.
wHma(source, weight, length)
Weighted HMA (linear kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Linear-kernel weighted mean; falls back to
classic HMA if Σweight = 0.
wRsi(source, weight, length)
Weighted Relative Strength Index.
Parameters:
source (float) : series float Price series.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Weighted RSI; uniform if Σw = 0.
wAtr(tr, weight, length)
Weighted ATR (Average True Range).
Implemented as WRMA on *true range*.
Parameters:
tr (float) : series float True Range series.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Weighted ATR; uniform weights if Σw = 0.
wTr(tr, weight, length)
Weighted True Range over a window.
Parameters:
tr (float) : series float True Range series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Weighted mean of TR; uniform if Σw = 0.
wR(r, weight, length)
Weighted High-Low Range over a window.
Parameters:
r (float) : series float High-Low per bar.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Weighted mean of range; uniform if Σw = 0.
wBtwVar(source, weight, length, biased)
Weighted Between Variance (biased/unbiased).
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns:
variance series float The calculated between-bar variance (σ²btw), either biased or unbiased.
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wBtwStdDev(source, weight, length, biased)
Weighted Between Standard Deviation.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float σbtw uniform if Σw = 0.
wBtwStdErr(source, weight, length, biased)
Weighted Between Standard Error.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float √(σ²btw / N_eff) uniform if Σw = 0.
wTotVar(mu, sigma, weight, length, biased)
Weighted Total Variance (= between-group + within-group).
Useful when each bar represents an aggregate with its own
mean* and pre-estimated σ (e.g., second-level ranges inside a
1-minute bar). Assumes the *weight* series applies to both the
group means and their σ estimates.
Parameters:
mu (float) : series float Group means (e.g., HL2 of 1-second bars).
sigma (float) : series float Pre-estimated σ of each group (same basis).
weight (float) : series float Weight series (volume, ticks, …).
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns:
varBtw series float The between-bar variance component (σ²btw).
varWtn series float The within-bar variance component (σ²wtn).
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wTotStdDev(mu, sigma, weight, length, biased)
Weighted Total Standard Deviation.
Parameters:
mu (float) : series float Group means (e.g., HL2 of 1-second bars).
sigma (float) : series float Pre-estimated σ of each group (same basis).
weight (float) : series float Weight series (volume, ticks, …).
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float σtot.
wTotStdErr(mu, sigma, weight, length, biased)
Weighted Total Standard Error.
SE = √( total variance / N_eff ) with the same effective sample
size logic as `wster()`.
Parameters:
mu (float) : series float Group means (e.g., HL2 of 1-second bars).
sigma (float) : series float Pre-estimated σ of each group (same basis).
weight (float) : series float Weight series (volume, ticks, …).
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float √(σ²tot / N_eff).
wLinReg(source, weight, length)
Weighted Linear Regression.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
Returns:
mid series float The estimated value of the regression line at the most recent bar.
slope series float The slope of the regression line.
intercept series float The intercept of the regression line.
wResVar(source, weight, midLine, slope, length, biased)
Weighted Residual Variance.
linear regression – optionally biased (population) or
unbiased (sample).
Parameters:
source (float) : series float Data series.
weight (float) : series float Weighting series (volume, etc.).
midLine (float) : series float Regression value at the last bar.
slope (float) : series float Slope per bar.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population variance (σ²_P), denominator ≈ N_eff.
false → sample variance (σ²_S), denominator ≈ N_eff - 2.
(Adjusts for 2 degrees of freedom lost to the regression).
Returns:
variance series float The calculated residual variance (σ²res), either biased or unbiased.
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wResStdDev(source, weight, midLine, slope, length, biased)
Weighted Residual Standard Deviation.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
midLine (float) : series float Regression value at the last bar.
slope (float) : series float Slope per bar.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float σres; uniform if Σw = 0.
wResStdErr(source, weight, midLine, slope, length, biased)
Weighted Residual Standard Error.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
midLine (float) : series float Regression value at the last bar.
slope (float) : series float Slope per bar.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float √(σ²res / N_eff); uniform if Σw = 0.
wLRTotVar(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Total Variance **around the
window’s weighted mean μ**.
σ²_tot = E_w ⟶ *within-group variance*
+ Var_w ⟶ *residual variance*
+ Var_w ⟶ *trend variance*
where each bar i in the look-back window contributes
m_i = *mean* (e.g. 1-sec HL2)
σ_i = *sigma* (pre-estimated intrabar σ)
w_i = *weight* (volume, ticks, …)
ŷ_i = b₀ + b₁·x (value of the weighted LR line)
r_i = m_i − ŷ_i (orthogonal residual)
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns:
varRes series float The residual variance component (σ²res).
varWtn series float The within-bar variance component (σ²wtn).
varTrd series float The trend variance component (σ²trd), explained by the linear regression.
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wLRTotStdDev(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Total Standard Deviation.
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √(σ²tot).
wLRTotStdErr(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Total Standard Error.
SE = √( σ²_tot / N_eff ) with N_eff = Σw² / Σw² (like in wster()).
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √((σ²res, σ²wtn, σ²trd) / N_eff).
wLRLocTotStdDev(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Local Total Standard Deviation.
Measures the total "noise" (within-bar + residual) around the trend.
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √(σ²wtn + σ²res).
wLRLocTotStdErr(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Local Total Standard Error.
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √((σ²wtn + σ²res) / N_eff).
wLSma(source, weight, length)
Weighted Least Square Moving Average.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
Returns: series float Least square weighted mean. Falls back
to unweighted regression if Σw = 0. Library
FunctionMatrixCovarianceLibrary "FunctionMatrixCovariance"
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector.
Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the `x` and `y` directions contain all of the necessary information; a `2 × 2` matrix would be necessary to fully characterize the two-dimensional variation.
Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself).
The covariance matrix of a random vector `X` is typically denoted by `Kxx`, `Σ` or `S`.
~wikipedia.
method cov(M, bias)
Estimate Covariance matrix with provided data.
Namespace types: matrix
Parameters:
M (matrix) : `matrix` Matrix with vectors in column order.
bias (bool)
Returns: Covariance matrix of provided vectors.
---
en.wikipedia.org
numpy.org Library
Variance WindowsJust a quick trial at using statistical variance/standard deviation as an indicator. The general idea is that higher variance in the short term tends to indicate more volatility/movement. The other thing is that it can help set probabilistic boundaries for movements (e.g., if you set the bars to be 2 standard deviations, you are visualizing a range that denotes a 95% probability window).
I haven't really tried forming any sort of strategies around this indicator, but there are a few potential possibilities for its usability.
Generally speaking, the magnitude of the standard deviation (relative to the price) is small when the market is consolidating. It is larger when the market is trending up or own.
If the long term variance and the short-term variance are close to each other in scale, the trend is strong. Otherwise, the trend is weak. Note that I am only saying that the "trend" is strong , not that it is necessarily positive. this could be an up-trend, down-trend, or a sideways trend.
When the magnitudes of the variances are changing from very similar to very different (usually it's the long-term variance getting much larger than the short-term one), that's an indication that the previous trend is coming to an end.
Typically, it's the long-term variance that is bigger than the short-term. However, when you see them cross where the short-term is bigger or even much bigger than the long-term, it's indicative of a spike event (more often than not, one that is not favorable if you are holding any position on a given security).
Because you have probabilistic windows based on some n standard deviations from the midline (which in this version, I've used a ZLEMA as that midline), those boundaries could possibly be used to set stop-loss limits and the like.
There's nothing too complicated or deep about this particular indicator. All I'm really doing is assuming that we are dealing with a Gaussian random process. I am actually using EMA as my mean computation, even though for a proper Gaussian variance calculation, I should be using SMA. When I used SMA, though, it felt a lot more sensitive to noise, which made it feel less usable. In any case, it's just a simple first trial in many years after not having even looked at Pine Script to finally messing around with it again. Open to a litany of criticisms as I'm sure there will be many that are rightly deserved. Otherwise, happy scalping to thee. Indicator
Indicator
Generalized Black-Scholes-Merton on Variance Form [Loxx]Generalized Black-Scholes-Merton on Variance Form is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options using variance instead of volatility.
Black- Scholes- Merton on Variance Form
In some circumstances, it is useful to rewrite the BSM formula using variance as input instead of volatility, V = v^2:
c = S * e^((b - r) * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^((b - r) * T) * N(-d1)
where
d1 = (log(S / X) + (b + V^2 / 2) * T) / (V * T)^0.5
d2 = d1 - (V * T)^0.5
BSM on variance form clearly gives the same price as when written on volatility form. The variance form is used indirectly in terms of its partial derivatives in some stochastic variance models, as well as for hedging of variance swaps. The BSM on variance form moreover admits an interesting symmetry between put and call options as discussed by Adamchuk and Haug (2005) at www.wilmott.com .
c(S, X, T, r, b, V) = -c(-S, -X, -T, -r, -b, -V)
and
p(S, X, T, r, b, V) = -p(-S, -X, -T, -r, -b, -V)
It is possible to find several similar symmetries if we introduce imaginary numbers.
b = r ... gives the Black and Scholes (1973) stock option model.
b = r — q ... gives the Merton (1973) stock option model with continuous dividend yield q.
b = 0 ... gives the Black (1976) futures option model.
b = 0 and r = 0 ... gives the Asay (1982) margined futures option model.
b = r — rf ... gives the Garman and Kohlhagen (1983) currency option model.
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
cc = Cost of Carry
V = Variance of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Indicator
Barndorff-Nielsen and Shephard Jump Statistic [Loxx]The following comments and descriptions are from from "Problems in the Application of Jump Detection Tests to Stock Price Data" by Michael William Schwert; Professor George Tauchen, Faculty Advisor.
This indicator applies several jump detection tests to intraday stock price data sampled at various frequencies. It finds that the choice of sampling frequency has an effect on both the amount of jumps detected by these tests, as well as the timing of those jumps. Furthermore, although these tests are designed to identify the same phenomenon, they find different amounts and timing of jumps when performed on the same data. These results suggest that these jump detection tests are probably identifying different types of jump behavior in stock price data, so they are not really substitutes for one another.
In recent years there has been a great deal of interest in studying jumps in asset price movements. Reasons why it is important to know when and how frequently jumps occur include risk management and the pricing and hedging of derivative contracts. Investors would benefit greatly from knowing the properties of jumps, since large instantaneous drops in asset prices result in large instantaneous losses. The effect of jumps on derivative pricing is equally significant, especially considering the important role derivatives play in modern financial markets. When asset price movements are continuous, investors can perfectly hedge derivative contracts such as options, but when jumps occur, they cause a change in the derivative price that is non-linear to the change in the price of the underlying asset. Thus, jumps introduce an unhedgeable risk to the holders of derivative contracts.
The ability to identify realized jumps in the financial markets could provide helpful information such as how frequently jumps occur, how large the jumps are, and whether they tend to occur in clusters. With this goal in mind, several authors have developed tests to determine whether or not an asset price movement is a statistically significant jump. These tests take advantage of the high-frequency intraday price data available today through electronic sources. Barndorff-Nielsen and Shephard (2004, 2006) use the difference between an estimate of variance and a jump-robust measure of variance to detect jumps over the course of a day. Approaching the problem differently, Jiang and Oomen (2007) exploit high order sample moments of returns to identify days that include jumps. Aїt-Sahalia and Jacod (2008) also exploit high order sample moments of returns to detect jumps by comparing price data sampled at two different frequencies. Lee and Mykland (2007) test for jumps at individual price observations by scaling returns by a local volatility measure. While these tests employ different strategies for detecting jumps, they are all designed to identify the same phenomenon.
For this indicator we are focused on the Barndorff-Nielsen and Shephard jump statistic.
Barndorff-Nielsen and Shephard (2004, 2006) developed a test that uses high-frequency price data to determine whether there is a jump over the course of a day. Their test compares two measures of variance: Realized Variance, which converges to the integrated variance plus a jump component as the time between observations approaches zero; and Bipower Variation, which converges to the integrated variance as the time between observations approaches zero, and is robust to jumps in the price path, an important fact for this application. The integrated variance of a price process is the integral of the square of the σ(t) term in (2.2.2), taken over the course of a day. Since prices cannot be observed continuously, one cannot calculate integrated variance exactly, and must estimate it instead.
For our purposes here, this is calculated as:
r = log(p /p )
This the geometric return from time ti-1 to time ti.
Then, Realized Variance and Bipower Variation are described by the following functions (see code for details)
realizedVariance(float src, int per)
and
bipowerVariance(float src, int per)
Huang and Tauchen (2005) also consider Relative Jump, a measure that approximates the percentage of total variance attributable to jumps:
RJ = (RV - BV) / RV
This statistic approximates the ratio of the sum of squared jumps to the total variance and is useful because it scales out long-term trends in volatility so one can compare the relative contribution of jumps to the variance of two price series with different volatilities.
To develop a statistical test to determine whether there is a significant difference between RV and BV, one needs an estimate of integrated quarticity. Andersen, Bollerslev, and Diebold (2004) recommend using a jump-robust realized Tri-Power Quarticity, I've included commentary in code to better explain how this indicator is collocated. See code for details.
How to use this indicator
When the bars turn gray, it's an indication that a jump has occurred in the market. It serves a warning that price jumped. I've included a percent point function (or inverse cumulative distribution function) to cutoff Z-score values depicted by histogram values. The top line at 3 is the empirical maximum Z-score value a serves merely as a point of reference. The Red line is the cutoff line calculated using PPF. When the histogram is green, no jumps have been detected. This indicator also includes alerts, signals, and bar coloring. I've also expanded the possible source types using my own Expanded Source Types library so you can test different log return methods as inputs. It is recommended to use window sizes of 7, 16, 78, 110, 156, and 270 returns for sampling intervals of 1 week, 1 day, 1 hour, 30 minutes, 15 minutes, and 5 minutes, respectively.
If you'ed like to better understand PPF, see here: Distributions in python
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Indicator
Indicator
Library
Indicator
GME REGIONAL PRICES OVERLAYGME Regional Prices Overlay (VWAP)
1. Select a chart 24-hour ticker like FX_IDC:USDEUR
2. Select a timescale (5 min, 15 min, ...)
3. Monitor the regional price variance
Exchanges included: NYSE, XETR, BMV, FWB, SWB, BITTREX, FTX, LSE, CAPITALCOM (CFD)
Currency conversion: FX_IDC Indicator
[BCT] Can BTC be predicted or is it purely random?Variance Ratio**This indicator can be applied to the ticker of your choice (not just BTC)**
Markets are said to be "efficient". An efficient market is by definition unpredictable - no matter the amount of ML, computation, or indicators thrown at it. In particular, in an efficient market, TA will not be of help.
An illustration of efficient markets is the WSJ's longstanding monkey vs. human contest:Blindfolded Monkey Beats Humans With Stock Picks, granted there are several flaws to it.
BTC is a relatively new market. New markets are typically highly inefficient (easier to make money) and become more and more efficient over time (harder to make money). How much more efficient is BTC becoming?
We apply the Variance Ratio method and apply it to BTC.
BACKGROUND ON THE VARIANCE RATIO METHOD
Based on 1988 MacKinlay's seminal paper "Stock Market Prices do not Follow a Random Walk", the idea is to exploit a phenomenon called "variance scaling".
For those keen on looking into the math, the short version of it is under the assumption of iid (random walk) we have the following:
H0: Var(Sum(returns over K bars))=Sum(Var(returns over 1 bar))=k*Var(return over 1 bar)
We look to reject or not H0 depending on the observations.
In this script, we compare the variance of the (log) returns for the chart selected between:
(1) The (average) variance over k bars (call this Vk)
(2) The (average) variance over 1 bar (call this V1)
H0 simply says that Vk=k*V1 if the stock follows a random walk.
We compute the Variance Ratio VR(k)=Variance(returns over k bar)/(Sum(Var(returns over 1 bar)))-1
We then compute the associated Z-score which we chart out for a configurable k number of bars.
HOW TO INTERPRET THE CHART
The line drawn is the Z-Score for VR(k). It represents the number of standard deviations of VR(k) from 0 - the further out, the less random.
- If the line is close / hovers around 0, the ticker appears to follow a random walk (i.e. may not be predictable)
- If the line is consistently > 2 or <-2, the ticker likely does not follow a random walk (i.e. may have predictable features)
- If the line is positive, it means that the Variance on the k bars is larger than the variance on 1 bar (more variance on longer timeframes)
- If the line is negative, it means that the Variance on the k bars is smaller than the variance on 1 bar (more variance on smaller timeframes)
USE CASES
- Identify timeframes where you won't be able to make money
- Identify whether a stock cannot be predicted (forget about TA, indicators etc. -- a random walk is not predictable)
- Identify whether a stock is becoming less and less predictable (Z-score amplitude will decrease over time)
FEATURES
- select the number of K bar to compare vs. 1 bar (default = 16) - ideally a power of 2 but any other number will work. The chart is based off this selection
- select the lookback period for the analysis (500 bars by default)
- select the source to analyze (default = close, but you may select other inputs to calculate the returns from)
- results form the statistical tests on different K's in the table on the right/bottom side of the chart (H0 rejected = not random walk; H0 not rejected = it essentially looks rather random and we can't conclude that it's not a random walk)
COMMENTARY ON BTC
- It appears BTC's absolute value of the ZScore on the Variance Ratio is declining year after year - corroborating an increasingly efficient market as new participants join.
- However, we can still detect a fair amount of potential inefficiency using this simple test.
As usual, this is not investment advice. DYOR.
With love,
🐵BCT🐵
Indicator
CV_VWAP_GMECoefficient of variance GME ‰
Gray area: Regional price variance of GME in per milles
Light gray thick line: NYSE:GME deviation from global mean
1. Select a chart 24-hour ticker like FX_IDC:USDEUR
2. Select a timescale (5 min, 15 min, ...)
3. Monitor the regional price variance
Exchanges included: NYSE, XETR, BMV, FWB, SWB, BITTREX, FTX
Currency conversion: Forex
Adapted from Detecting the great short squeeze on Volkswagen, Godfrey, K. (2016, February 18). Indicator
Indicator
Risk Metrics: beta 'β', correl 'ρxy', stdev 'σ', variance 'σ²'Portfolio Risk Metrics (Part I):
beta 'β'
The beta coefficient can be interpreted as follows:
β =1 exactly as volatile as the market
β >1 more volatile than the market
β <1>0 less volatile than the market
β =0 uncorrelated to the market
β <0 negatively correlated to the market
excerpt from the Corporate Finance Institute
correlation coefficient 'ρxy'
The correlation coefficient is a value that indicates the strength of the relationship between variables.
The coefficient can take any values from -1 to 1. The interpretations of the values are:
-1: Perfect negative correlation. The variables tend to move in opposite directions
(i.e., when one variable increases, the other variable decreases).
0: No correlation. The variables do not have a relationship with each other.
1: Perfect positive correlation. The variables tend to move in the same direction
(i.e., when one variable increases, the other variable also increases).
excerpt from the Corporate Finance Institute
standard deviation 'σ'
68% of returns will fall within 1 standard deviation of the arithmetic mean
95% of returns will fall within 2 standard deviations of the arithmetic mean
99% of returns will fall within 3 standard deviations of the arithmetic mean
excerpt from Corporate Finance Institute
variance 'σ²'
In investing, variance is used to compare the relative performance of each asset in a portfolio.
Because the results can be difficult to analyze, standard deviation is often used instead of variance.
In either case, the goal for the investor is to improve asset allocation.
excerpt from Investopedia
Indicator
Garch (1,1) ModelThe Garch (General Autoregressive Conditional Heteroskedasticity) model is a non-linear time series model that uses past data to forecast future variance.
The Garch (1,1) formula is:
Garch = (gamma * Long Run Variance) + (alpha * Squared Lagged Returns) + (beta * Lagged Variance)
The gamma, alpha, and beta values are all weights used in the Garch calculations. According to RiskMetrics by JP Morgan, the optimal beta weight is 0.94, but this figure is highly disputed in the academic realm. The biggest problem academics and economists have with the 0.94 figure is that JP Morgan used monthly data to come to this number, meaning it does not take other time frames into account. Because of the disputed nature of what beta should be, this script will automatically calculate the beta weight for you in real time, taking into account the time frame you're using and realized variance, by using the Minimum Sum of Squared Errors Method.
The gamma and alpha weights are also calculated for you.
Even though the Garch formula provides today's projected variance, today's projected deviation is also calculated. This is done by taking the square root of Garch.
Additionally, if you want to project the variance or deviation for as many days forward as you want, you can.
In order to project the variance and deviation beyond just today, these equations are used:
Projected Variance = Long Run Variance + (alpha + beta)^Days Forward * (Garch - Long Run Variance)
Projected Deviation = sqrt(Projected Variance)
How to use this model:
1st. Decide the type of data you want: Projected Variance in % or Projected Deviation in %.
2nd. Decide how many days you want projected forward. If you input 0, you will get projections for today. If you input 1, you will get projections for tomorrow, and etc.
That's it. If you have any further questions, I left detailed comments in the code explaining each step, as best as I could. Indicator
Minimum Variance SMAReturn the value of a simple moving average with a period within the range min to max such that the variance of the same period is the smallest available.
Since the smallest variance is often the one with the smallest period, a penalty setting is introduced, and allows the indicator to return moving averages values with higher periods more often, with higher penalty values returning moving averages values with higher periods.
Because variances with smaller periods are more reactive than ones with higher periods, it is common for the indicator to return the value of an SMA of a higher period during more volatile market, this can be seen on the image below:
here variances from period 10 to 15 are plotted, a blueish color represents a higher period, note how they are the smallest ones when fluctuations are more volatile.
Indicator with min = 50, max = 200 and penalty = 0.5
In blue the indicator with penalty = 0, in red with penalty = 1, with both min = 50 and max = 200.
On The Script
The script minimize Var(i)/p with i ∈ (min,max) and p = i^penalty , this is done by computing the variance for each period i and keeping the smallest one currently in the loop, if we get a variance value smaller than the previously one found we calculate the value of an SMA with period i , as such the script deal with brute force optimization.
For our use case it is not possible to use the built-in sma and variance functions within a loop, as such we use cumulative forms for both functions. Indicator
Functions Allowing Series As Length - PineCoders FAQ█ WARNING
Improvements to the following Pine built-ins have deprecated the vast majority of this publication's functions, as the built-ins now accept "series int" `length` arguments:
ta.wma()
ta.linreg()
ta.variance()
ta.stdev()
ta.correlation()
NOTE
For an EMA function that allows a "series int" argument for `length`, please see `ema2()` in the ta library by PulseWire .
█ ORIGINAL DESCRIPTION
Pinescript requires many of its built-in functions to use a simple int as their period length, which entails the period length cannot vary during the script's execution. These functions allow using a series int or series float for their period length, which means it can vary on each bar.
The functions shared in this script include:
Rolling sum: Sum(src,p)
Simple moving average: Sma(src,p)
Rolling variance: Variance(src,p)
Rolling standard deviation: Stdev(src,p)
Rolling covariance: Covariance(x,y,p)
Rolling correlation: Correlation(x,y,p)
If p is a float then it is rounded to the nearest int .
How to Use the Script
Most of the functions in the script are dependent on the Sma function. The Correlation function uses the Covariance and Stdev functions. Be sure you include all the required functions in your script.
Make sure the series you use as the length argument is greater than 0, else the functions will return na . When using a series as length argument, the following error might appear:
Pine cannot determine the referencing length of a series. Try using max_bars_back in the study or strategy function.
This can be frequent if you use barssince(condition) where condition is a relatively rare event. You can fix it by including max_bars_back=5000 in your study declaration statement as follows:
study("Title",overlay=true,max_bars_back=5000)
Example
The chart shows the Sma , Stdev , Covariance and Correlation functions. The Sma uses the closing price as input and bars as period length where:
bars = barssince(change(security(syminfo.tickerid,"D",close ,lookahead=true)))
The Stdev uses the closing price as input and bars + 9 as period length. The Covariance and Correlation use the closing price as x and bar_index as y , with bars + 9 as period length.
Look first. Then leap.
Indicator
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