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RandomWalkIndex

Incremental, causal technical analysis documentation

Summary

RandomWalkIndex is RTTA's streaming Random Walk Index (RWI). It compares the current high/low extremes against the window's opposite extreme, scaled by ATR times \(\sqrt{n}\), yielding separate high-side and low-side readings.

Update API

result = rtta.RandomWalkIndex(window=14, fillna=True).update(close, high, low)
# result.high, result.low

With fillna=False, both fields are NaN until window samples have been seen.

Theory Of Operation

The Random Walk Index asks whether price has moved farther than a random walk would typically travel over \(n\) bars. Under a simple diffusion model, expected distance grows like \(\sigma\sqrt{n}\); ATR stands in for \(\sigma\). When RWI High is large, the market has advanced more than random-walk noise from the window low; when RWI Low is large, it has declined more than noise from the window high. Values above roughly 1 are often interpreted as non-random trend evidence on that side.

Recurrence

Let \(C_t, H_t, L_t\) be close, high, low and \(n\) be window (default \(14\)).

Maintain a rolling maximum of highs and rolling minimum of lows over \(n\) bars, and Wilder ATR over the same length:

\[H^{\max}_t = \max_{0\le i < n} H_{t-i}, \qquad L^{\min}_t = \min_{0\le i < n} L_{t-i}\]
\[A_t = \operatorname{ATR}_n(C_t, H_t, L_t)\]
\[\operatorname{scale}_t = A_t \sqrt{n}\]
\[\begin{aligned} \operatorname{RWI\text{-}High}_t &= \frac{H_t - L^{\min}_t}{\operatorname{scale}_t} \\ \operatorname{RWI\text{-}Low}_t &= \frac{H^{\max}_t - L_t}{\operatorname{scale}_t} \end{aligned}\]

(safe divide). Result field high is RWI-High; field low is RWI-Low. Nested ATR uses fillna=True.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class RandomWalkIndex using RollingExtreme highs/lows and ATR.

Reference