PageHinkley

Summary

PageHinkley is RTTA's streaming implementation of: Causal Page-Hinkley mean-shift event detector with directed up/down output.

Update API

result = rtta.PageHinkley(threshold=1.0, delta=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

PageHinkley tracks cumulative positive and negative deviations from an online mean after subtracting a small drift allowance. A signal fires when one cumulative excursion rises far enough above its own running minimum; the detector then resets to the current close.

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.

\[\mu_t=\mu_{t-1}+\frac{close_t-\mu_{t-1}}{t}\]

\[P_t=P_{t-1}+close_t-\mu_t-\delta, \qquad N_t=N_{t-1}+\mu_t-close_t-\delta\]

\[S^+_t=P_t-\min_{i\le t}P_i, \qquad S^-_t=N_t-\min_{i\le t}N_i\]

\[y_t = \begin{cases} 1, & S^+_t > h \text{ and } S^+_t \ge S^-_t\\ -1, & S^-_t > h\\ 0, & \text{otherwise} \end{cases}\]

After a nonzero signal the C++ implementation resets the running mean and cumulative sums to the current close.

The return value is the current scalar indicator value.

Implementation Notes

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

Reference

Background reference