PairsSpreadRegimeDetector

Summary

PairsSpreadRegimeDetector is RTTA's streaming implementation of: Streaming EWMA hedge-ratio residual z-score detector for pair-spread regimes.

Update API

result = rtta.PairsSpreadRegimeDetector().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

PairsSpreadRegimeDetector 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.

\[\beta_t=\frac{C^{xy}_t}{V^y_t}, \qquad \alpha_t=\mu^x_t-\beta_t\mu^y_t\]

\[e_t=x_t-(\beta_t y_t+\alpha_t), \qquad q_t=\frac{e_t-\bar{e}_{t-1}}{\sqrt{\max(s^2_{e,t-1},\epsilon)}}\]

\[\bar{e}_t=\bar{e}_{t-1}+\eta(e_t-\bar{e}_{t-1}), \qquad s^2_{e,t}=(1-\eta)(s^2_{e,t-1}+\eta(e_t-\bar{e}_{t-1})^2)\]

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

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 PairsSpreadRegimeDetector.

Reference

Background reference