Indicator Rwi

RWI

Mike Poulos' Random Walk Index — measures how many standard deviations the current move is away from a random walk of the same length. Higher RWI means the directional move is statistically more significant than noise.

Quick reference

Field	Value
Family	Trend & Directional
Input type	Candle
Output type	RwiOutput { high, low }
Output range	>= 0 (each line)
Default parameters	period = 14 (must be >= 2)
Warmup period	period
Interpretation	RWI_High > 1 and dominant = real uptrend; mirror for downtrend. Both lines below 1 = ranging.

Formula

For each lookback i ∈ [2, period]:

RWI_High_t(i) = (high_t       − low_{t-i+1})  / (ATR_i(t) * sqrt(i))
RWI_Low_t(i)  = (high_{t-i+1} − low_t)        / (ATR_i(t) * sqrt(i))

where ATR_i(t) is the simple mean of true-range over the most recent i bars. The per-bar emission is the maximum of these ratios across all lookbacks i ∈ [2, period]:

RWI_High_t = max_{i ∈ [2, period]} RWI_High_t(i)
RWI_Low_t  = max_{i ∈ [2, period]} RWI_Low_t(i)

A flat window (zero ATR) short-circuits each lookback to zero, so the indicator reports (0, 0) on a perfectly motionless market.

Parameters

Name	Type	Default	Valid range	Description
period	usize	14	>= 2	Max lookback. period < 2 returns Error::InvalidPeriod because lookback i = 2 is the shortest meaningful comparison.

Interpretation

• RWI_High crossing above RWI_Low signals a fresh uptrend.
• RWI_High > 2 is the typical "strong trend" threshold used by Poulos in the original 1991 Stocks & Commodities article.
• Both lines < 1 — neither direction beats random-walk noise; treat the market as ranging and avoid trend-following signals.

Reference

E. Michael Poulos, "Of Trends and Random Walks", Technical Analysis of Stocks & Commodities, February 1991 — original publication of the indicator. The sqrt(i) denominator comes from the expectation that a random walk of i steps drifts a distance proportional to sqrt(i).

See also

• Adx — alternative trend-strength gauge, smoothed rather than threshold-based.
• ChoppinessIndex — log-scaled trend-vs.-range complement.
• Warmup Periods — the period RWI entry.