EWMAZScoreShiftDetector

Summary

EWMAZScoreShiftDetector is RTTA's streaming implementation of: Causal EWMA mean/variance z-score event detector for threshold-sized shifts.

Update API

result = rtta.EWMAZScoreShiftDetector(alpha=0.05, threshold=3.0).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

EWMAZScoreShiftDetector standardizes the current error or move against an EWMA mean and variance estimated from prior samples. The detector uses the resulting z-score with hysteresis or reset logic so isolated noisy observations do not become persistent regimes by themselves.

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.

\[z_t=\frac{close_t-\mu_{t-1}}{\sqrt{\max(\sigma^2_{t-1},\epsilon)}}\]

\[y_t = \begin{cases} 1, & z_t>h\\ -1, & z_t<-h\\ 0, & \text{otherwise} \end{cases}\]

\[\mu_t=\mu_{t-1}+\alpha(close_t-\mu_{t-1}), \qquad \sigma^2_t=(1-\alpha)(\sigma^2_{t-1}+\alpha(close_t-\mu_{t-1})^2)\]

When \(y_t\ne0\), the C++ implementation resets \(\mu_t\) to the current close and clears the variance estimate.

The return value is the current scalar indicator value.

Implementation Notes

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

Reference

Background reference