RWI

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

Quick reference

Field	Value
Family	Trend & Directional
Input type	Candle (uses high, low, close)
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 < 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 across all lookbacks:

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

The sqrt(i) denominator comes from the expectation that a random walk of i steps drifts a distance proportional to sqrt(i); dividing the actual displacement by it measures how far the real move exceeds random noise.

Parameters

Name	Type	Default	Constraint	Source
period	usize	14	>= 2	Rwi::new (rwi.rs:78)

period == 0 returns [Error::PeriodZero]; period < 2 returns [Error::InvalidPeriod] (lookback i = 2 is the shortest meaningful comparison). Python default comes from #[pyo3(signature = (period=14))]; the Node constructor takes period explicitly. The public class is RWI in both bindings.

Inputs / Outputs

use wickra::{Indicator, Rwi, Candle, RwiOutput};
// Rwi: Input = Candle, Output = RwiOutput
const _: fn(&mut Rwi, Candle) -> Option<RwiOutput> = <Rwi as Indicator>::update;

• Python. update(candle) returns (high, low) or None; batch(high, low, close) returns an (n, 2) np.ndarray with columns [high, low]; warmup rows are NaN.
• Node. update(high, low, close) returns a { high, low } object or null; batch(high, low, close) returns a flat Array<number> of length 2n, interleaved [high0, low0, …].

Warmup

warmup_period() returns period: the rolling window must hold period candles before the lookbacks i ∈ [2, period] can be scanned, so the first output lands on candle period (index period − 1). Pinned by first_emission_at_warmup_period.

Edge cases

• Flat market. Zero ATR short-circuits every lookback (denominator guard), so RWI reports (0, 0) (test constant_series_yields_zero_outputs).
• Pure uptrend. RWI_High dominates RWI_Low and exceeds 1 (test pure_uptrend_high_dominates_low); the downtrend mirror holds (test pure_downtrend_low_dominates_high).
• Non-negative & finite. Both lines are always >= 0 and finite (test outputs_non_negative).
• Reset. reset() clears the candle and true-range windows.

Examples

Rust

use wickra::{BatchExt, Candle, Indicator, Rwi};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let candles: Vec<Candle> = (0..40)
        .map(|i| {
            let base = 100.0 + f64::from(i) * 2.0; // clean uptrend
            Candle::new(base, base + 1.0, base - 0.5, base + 0.5, 1.0, i64::from(i)).unwrap()
        })
        .collect();
    let mut r = Rwi::new(14)?;
    if let Some(o) = r.batch(&candles).into_iter().flatten().last() {
        println!("high={:.3} low={:.3}", o.high, o.low); // high >> low on an uptrend
    }
    Ok(())
}

Python

import numpy as np
import wickra as ta

r = ta.RWI(14)
out = r.batch(high, low, close)  # shape (n, 2): [high, low]
rwi_high, rwi_low = out[:, 0], out[:, 1]

Node

const ta = require('wickra');
const r = new ta.RWI(14);
const o = r.update(102, 98, 101); // high, low, close → { high, low } or null

Interpretation

RWI asks, for the strongest lookback, "is this move bigger than a random walk would produce?":

1. Trend confirmation. RWI_High above RWI_Low and above 1 marks a statistically real uptrend; the mirror marks a downtrend. Poulos' strong- trend threshold is > 2.
2. Range filter. Both lines below 1 mean neither direction beats noise — treat the market as ranging and suppress trend-following signals.

Common pitfalls

• Reading the two lines as a single oscillator. They are independent bull/bear strengths; the relationship (which is larger, and whether it clears 1) is the signal, not either value alone.
• Using period = 1. The shortest lookback is i = 2, so the constructor rejects it.

References

• E. Michael Poulos, "Of Trends and Random Walks", Technical Analysis of Stocks & Commodities, February 1991.

See also

• Adx — smoothed trend-strength gauge.
• Adxr — averaged ADX.
• ChoppinessIndex — log-scaled trend-vs-range complement.