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KSWIN

Incremental, causal technical analysis documentation

Summary

KSWIN is RTTA's streaming implementation of: Kolmogorov-Smirnov sliding-window drift detector.

Update API

result = rtta.KSWIN().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

KSWIN compares the empirical distribution of a recent subwindow with the older reference portion of the rolling window using the Kolmogorov-Smirnov supremum distance. The output direction is determined by which subwindow has the larger mean when the KS statistic clears its critical value.

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.

\[A_t=W_t[1:|W_t|-m], \qquad B_t=W_t[|W_t|-m+1:|W_t|]\]
\[D_t=\sup_x |\widehat{F}_{A_t}(x)-\widehat{F}_{B_t}(x)|\]
\[c_\alpha=\sqrt{-\frac{1}{2}\log(\alpha/2) \left(\frac{1}{|A_t|}+\frac{1}{|B_t|}\right)}\]
\[y_t = \begin{cases} \operatorname{sgn}(\bar{B}_t-\bar{A}_t), & D_t>c_\alpha\\ 0, & \text{otherwise} \end{cases}\]

The return value is the current scalar indicator value.

Implementation Notes

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

Reference