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CUSUM

Incremental, causal technical analysis documentation

Summary

CUSUM is RTTA's streaming implementation of: Causal cumulative-sum event filter for detecting threshold-sized directional moves.

Update API

result = rtta.CUSUM(threshold=1.0, drift=0.0).update(close)

The update(...) call consumes one observation using close. advance(...) uses the same inputs when the caller wants to update state without materializing a Python return value.

Theory Of Operation

CUSUM implements the streaming form of Causal cumulative-sum event filter for detecting threshold-sized directional moves. Each update(...) call consumes exactly one new observation tuple and advances the internal state before returning the current value or result struct.

Recurrence

Let \(z_t = close_t\) denote the observation consumed by one update(...) call and let \(\theta\) denote constructor parameters such as window lengths, thresholds, and smoothing constants.

\[\Delta_t=close_t-close_{t-1}\]
\[S^+_t=\max(0,S^+_{t-1}+\Delta_t-\kappa), \qquad S^-_t=\min(0,S^-_{t-1}+\Delta_t+\kappa)\]
\[y_t=\begin{cases}1,&S^+_t>h\\-1,&S^-_t<-h\\0,&\text{otherwise}\end{cases}\]

The return value is the current scalar indicator value.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class CUSUM.

Reference