LeadLagRegimeDetector

Summary

LeadLagRegimeDetector is RTTA's streaming implementation of: EWMA cross-lag detector for which of two series is leading.

Update API

result = rtta.LeadLagRegimeDetector().update(real0, real1)

The update(...) call consumes one observation using real0, real1. advance(...) uses the same inputs when the caller wants to update state without materializing a Python return value.

Theory Of Operation

LeadLagRegimeDetector first constructs a scalar market-state metric from the current observation and compact streaming state, then passes that metric through explicit entry/exit hysteresis. The metric is named in the recurrence below; the hysteresis keeps the output stable until the metric crosses the opposite exit band.

Recurrence

Let \(z_t = (real0_t, real1_t)\) denote the observation consumed by one update(...) call and let \(\theta\) denote constructor parameters such as window lengths, thresholds, and smoothing constants.

\[\Delta x_t=x_t-x_{t-1}, \qquad \Delta y_t=y_t-y_{t-1}\]

\[a_t=\Delta x_{t-1}\Delta y_t, \qquad b_t=\Delta y_{t-1}\Delta x_t\]

\[S_t=\alpha(a_t-b_t)+(1-\alpha)S_{t-1}, \qquad C_t=\alpha(|a_t|+|b_t|)+(1-\alpha)C_{t-1}\]

\[q_t=\frac{S_t}{\max(C_t,\epsilon)}\]

\[r_t = \begin{cases} 1, & r_{t-1} \le 0 \text{ and } q_t \ge u_e \\ 0, & r_{t-1} = 1 \text{ and } q_t \le u_x \\ -1, & r_{t-1} \ge 0 \text{ and } q_t \le \ell_e \\ 0, & r_{t-1} = -1 \text{ and } q_t \ge \ell_x \\ r_{t-1}, & \text{otherwise} \end{cases}\]

The entry/exit constants satisfy \(\ell_e < \ell_x \le u_x < u_e\).

The return value is the current scalar indicator value.

Implementation Notes

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

Reference

Background reference