RollingMeanVarianceShiftDetector

Summary

RollingMeanVarianceShiftDetector is RTTA's streaming implementation of: Causal adjacent-window combined mean and variance shift detector.

Update API

result = rtta.RollingMeanVarianceShiftDetector(window=20, 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

RollingMeanVarianceShiftDetector compares two adjacent rolling windows: a reference window and a recent window. The C++ state moves expired recent samples into the reference window, maintains sufficient statistics, and emits the sign of the statistic difference when it exceeds the configured threshold.

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.

\[z^\mu_t=\frac{\bar{x}^{R}_t-\bar{x}^{B}_t} {\sqrt{\sigma^{2,R}_t/n+\sigma^{2,B}_t/n+\epsilon}}, \qquad z^\sigma_t=\log\left(\frac{\sigma^{2,R}_t+\epsilon}{\sigma^{2,B}_t+\epsilon}\right)\]

\[q_t=\sqrt{(z^\mu_t)^2+w(z^\sigma_t)^2}, \qquad d_t=\begin{cases} z^\mu_t, & |z^\mu_t|\ge |\sqrt{w}z^\sigma_t|\\ \sqrt{w}z^\sigma_t, & \text{otherwise} \end{cases}\]

\[y_t = \begin{cases} \operatorname{sgn}(d_t), & q_t>h\\ 0, & \text{otherwise} \end{cases}\]

The return value is the current scalar indicator value.

Implementation Notes

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

Reference

Background reference