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ADWIN

Incremental, causal technical analysis documentation

Summary

ADWIN is RTTA's streaming implementation of: Adaptive-window mean drift detector with bounded history and directed shift output.

Update API

result = rtta.ADWIN().update(value)

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

Theory Of Operation

ADWIN maintains an adaptive recent window and searches every admissible split for a statistically meaningful difference between the old and new subwindow means. The signal direction is the sign of the best accepted mean shift; accepting a split discards the older prefix.

Recurrence

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

\[W_t=\operatorname{tail}_{max\_window}(W_{t-1}\cup\{x_t\})\]
\[\epsilon(c)=R_t \sqrt{\frac{1}{2}\log\left(\frac{4}{\delta}\right) \left(\frac{1}{c}+\frac{1}{|W_t|-c}\right)}\]
\[c^\*=\arg\max_c |\bar{x}_{c:|W_t|}-\bar{x}_{1:c}| \quad \text{s.t.}\quad |\bar{x}_{c:|W_t|}-\bar{x}_{1:c}|>\epsilon(c)\]
\[y_t = \begin{cases} \operatorname{sgn}(\bar{x}_{c^\*:|W_t|}-\bar{x}_{1:c^\*}), & c^\* \text{ exists}\\ 0, & \text{otherwise} \end{cases}\]

When a cut is accepted, the older prefix is discarded and the retained suffix becomes the next adaptive window.

The return value is the current scalar indicator value.

Implementation Notes

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

Reference