OPEN-SOURCE SCRIPT
Brownian Motion Residual [JOAT]
BROWNIAN MOTION RESIDUAL [JOAT]
A regime classifier rooted in the sqrt(T) scaling law of geometric Brownian motion. Under a true random walk, the standard deviation of T-bar returns scales as σ₁ · √T — that is the central fact of Brownian motion in continuous time. Markets violate this scaling in revealing ways: when they trend, dispersion at long horizons grows faster than √T; when they mean-revert, it grows slower. Brownian Motion Residual measures that violation across three horizons simultaneously, aggregates it, and surfaces a single Z-like residual that classifies the market into Strong MR / MR / Random / Trend / Strong Trend.
The sqrt(T) scaling law, restated
For a Brownian process with per-bar volatility σ₁:
σ(T-bar return) = σ₁ · √T
For a real market the observed σ at horizon T can be measured directly. The residual is the deviation of the observed value from the Brownian-implied value:
residual(T) = σ_observed(T) − σ₁ · √T
When the residual is positive, dispersion at T is greater than Brownian predicts — the market is trending (price travels further than a random walk in T bars). When it is negative, dispersion is less than Brownian predicts — the market is mean-reverting (price ends up closer to home than a random walk would).
Optional normalisation by σ₁ · √T turns the residual into a unit-less percentage of expected dispersion, so the same threshold values are meaningful across instruments and timeframes.
Three horizons, weighted blend
A single horizon is noisy. Brownian Motion Residual reads three horizons simultaneously (default 5 / 20 / 100 bars), each independently toggleable and weighted (default 1.0 each). The horizons are aggregated into a single residual line — the script's headline metric. Toggling off the short horizon makes the read smoother and slower; toggling off the long horizon makes it more reactive. Configurable.
A configurable EMA on top of the aggregated residual suppresses single-bar noise without lagging the regime view.
Two-tier classification
The aggregated residual is mapped to one of five regimes by two symmetric thresholds (default ±1 mild, ±2 strong):
Visual system
A locked Aurora palette (teal trend / lavender MR / mint random on a deep-night ground) gives the pane a distinctive structural identity.
Dashboard
Monospaced table, positionable to any of nine corners, with vertical row-fade. Surfaces:
Optional fancy Unicode header for the institutional aesthetic.
Alerts
Three alert conditions, each independently controllable:
How to read it
Three reads, in order of conviction:
Suggested settings
Defaults (σ₁ window 100, observed σ window 60, horizons 5/20/100, equal weights, log returns ON, normalisation ON) are tuned for 15m–4H on liquid markets. For lower timeframes drop horizon 3 to 50. For HTF (daily+) raise horizon 3 to 200 and σ₁ window to 200. Log returns are theoretically correct and the recommended default — the script's regime classification depends on the scaling law, which assumes log returns; switch off only for research.
Originality
The √T Brownian scaling law is textbook continuous-time finance — the central piece of Bachelier's 1900 thesis and the foundation of every diffusion model in pricing. The implementation here — the per-horizon σ measurement pipeline, the σ₁-anchored Brownian baseline with optional normalisation, the three-horizon weighted aggregation, the EMA-smoothed residual classifier with two-tier thresholds, the per-horizon overlay layer, the regime-tinted background, and the dashboard — is JOAT-original. No third-party code reused. The use of residual against Brownian as a regime classifier is the original quantitative contribution.
Limitations
The √T law is exact only for Brownian motion — real markets have fat tails, autocorrelation, and discrete bars, so the measured "residual" is always non-zero even in a regime that looks random. The thresholds (±1 / ±2) are calibrated to be the regime boundaries empirically; tighten or loosen if your instrument has unusual variance behaviour. Per-horizon σ values need their respective windows populated to be meaningful — early bars give a warm-up read.
—
-made with passion by jackofalltrades
A regime classifier rooted in the sqrt(T) scaling law of geometric Brownian motion. Under a true random walk, the standard deviation of T-bar returns scales as σ₁ · √T — that is the central fact of Brownian motion in continuous time. Markets violate this scaling in revealing ways: when they trend, dispersion at long horizons grows faster than √T; when they mean-revert, it grows slower. Brownian Motion Residual measures that violation across three horizons simultaneously, aggregates it, and surfaces a single Z-like residual that classifies the market into Strong MR / MR / Random / Trend / Strong Trend.
The sqrt(T) scaling law, restated
For a Brownian process with per-bar volatility σ₁:
σ(T-bar return) = σ₁ · √T
For a real market the observed σ at horizon T can be measured directly. The residual is the deviation of the observed value from the Brownian-implied value:
residual(T) = σ_observed(T) − σ₁ · √T
When the residual is positive, dispersion at T is greater than Brownian predicts — the market is trending (price travels further than a random walk in T bars). When it is negative, dispersion is less than Brownian predicts — the market is mean-reverting (price ends up closer to home than a random walk would).
Optional normalisation by σ₁ · √T turns the residual into a unit-less percentage of expected dispersion, so the same threshold values are meaningful across instruments and timeframes.
Three horizons, weighted blend
A single horizon is noisy. Brownian Motion Residual reads three horizons simultaneously (default 5 / 20 / 100 bars), each independently toggleable and weighted (default 1.0 each). The horizons are aggregated into a single residual line — the script's headline metric. Toggling off the short horizon makes the read smoother and slower; toggling off the long horizon makes it more reactive. Configurable.
A configurable EMA on top of the aggregated residual suppresses single-bar noise without lagging the regime view.
Two-tier classification
The aggregated residual is mapped to one of five regimes by two symmetric thresholds (default ±1 mild, ±2 strong):
- Strong Trend — residual > +2. Aggressive momentum regime.
- Trend — residual between +1 and +2. Trending.
- Random — residual between −1 and +1. Brownian-like.
- MR — residual between −2 and −1. Mean-reverting.
- Strong MR — residual < −2. Aggressive reversion regime.
Visual system
- Slope-coloured residual line with configurable width and optional area fill under it (transparency configurable).
- Zero line and ±1 / ±2 threshold lines (toggleable).
- Background tint by regime (subtle 88 transparency default) — teal trend, lavender MR, mint random.
- Per-horizon plots (toggleable, off by default) — each horizon's residual as a faint dotted overlay; useful for seeing which horizon is driving the read.
- Regime-change dots above the line at every confirmed flip.
A locked Aurora palette (teal trend / lavender MR / mint random on a deep-night ground) gives the pane a distinctive structural identity.
Dashboard
Monospaced table, positionable to any of nine corners, with vertical row-fade. Surfaces:
- Aggregated residual (raw and smoothed).
- Regime classification with glyph.
- σ₁ value (the Brownian anchor).
- Per-horizon residuals (h1 / h2 / h3) when enabled.
- Bars in current regime.
- Distance to nearest threshold.
Optional fancy Unicode header for the institutional aesthetic.
Alerts
Three alert conditions, each independently controllable:
- Regime Change (any classification flip)
- Strong threshold cross (±2)
- Mild threshold cross (±1) — off by default
How to read it
Three reads, in order of conviction:
- Strong Trend / Strong MR entry — the highest-conviction read. The market has decisively departed from Brownian scaling in one direction. Pair with a momentum tool in Trend regimes, a reversion tool in MR regimes.
- Residual crossing zero — the regime fault line. Even before crossing a threshold, a sustained sign flip means the underlying distribution has rotated; the next threshold cross will confirm the new regime.
- Per-horizon disagreement (when enabled) — when the short horizon is in trend regime but the long horizon is in MR regime, the market is in a nested state: short-term momentum inside a longer reversion. This is the textbook setup for fade-the-extreme intraday plays inside a wider range.
Suggested settings
Defaults (σ₁ window 100, observed σ window 60, horizons 5/20/100, equal weights, log returns ON, normalisation ON) are tuned for 15m–4H on liquid markets. For lower timeframes drop horizon 3 to 50. For HTF (daily+) raise horizon 3 to 200 and σ₁ window to 200. Log returns are theoretically correct and the recommended default — the script's regime classification depends on the scaling law, which assumes log returns; switch off only for research.
Originality
The √T Brownian scaling law is textbook continuous-time finance — the central piece of Bachelier's 1900 thesis and the foundation of every diffusion model in pricing. The implementation here — the per-horizon σ measurement pipeline, the σ₁-anchored Brownian baseline with optional normalisation, the three-horizon weighted aggregation, the EMA-smoothed residual classifier with two-tier thresholds, the per-horizon overlay layer, the regime-tinted background, and the dashboard — is JOAT-original. No third-party code reused. The use of residual against Brownian as a regime classifier is the original quantitative contribution.
Limitations
The √T law is exact only for Brownian motion — real markets have fat tails, autocorrelation, and discrete bars, so the measured "residual" is always non-zero even in a regime that looks random. The thresholds (±1 / ±2) are calibrated to be the regime boundaries empirically; tighten or loosen if your instrument has unusual variance behaviour. Per-horizon σ values need their respective windows populated to be meaningful — early bars give a warm-up read.
—
-made with passion by jackofalltrades
Open-source Skript
Ganz im Sinne von TradingView hat dieser Autor sein/ihr Script als Open-Source veröffentlicht. Auf diese Weise können nun auch andere Trader das Script rezensieren und die Funktionalität überprüfen. Vielen Dank an den Autor! Sie können das Script kostenlos verwenden, aber eine Wiederveröffentlichung des Codes unterliegt unseren Hausregeln.
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Haftungsausschluss
Die Informationen und Veröffentlichungen sind nicht als Finanz-, Anlage-, Handels- oder andere Arten von Ratschlägen oder Empfehlungen gedacht, die von TradingView bereitgestellt oder gebilligt werden, und stellen diese nicht dar. Lesen Sie mehr in den Nutzungsbedingungen.
Open-source Skript
Ganz im Sinne von TradingView hat dieser Autor sein/ihr Script als Open-Source veröffentlicht. Auf diese Weise können nun auch andere Trader das Script rezensieren und die Funktionalität überprüfen. Vielen Dank an den Autor! Sie können das Script kostenlos verwenden, aber eine Wiederveröffentlichung des Codes unterliegt unseren Hausregeln.
The AI Trading Ecosystem, Built to win trades 📈
Get Full Access 👇
jackofalltrades.vip 🌐
t.me/jackofalltradesvip 🃏
Get Full Access 👇
jackofalltrades.vip 🌐
t.me/jackofalltradesvip 🃏
Haftungsausschluss
Die Informationen und Veröffentlichungen sind nicht als Finanz-, Anlage-, Handels- oder andere Arten von Ratschlägen oder Empfehlungen gedacht, die von TradingView bereitgestellt oder gebilligt werden, und stellen diese nicht dar. Lesen Sie mehr in den Nutzungsbedingungen.