Correlation

Summary

Correlation is RTTA's streaming implementation of: Rolling Pearson correlation between two series.

Update API

result = rtta.Correlation().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

Correlation keeps rolling sufficient statistics for the requested statistical quantity. Each update inserts the newest sample, removes any expired sample, and recomputes the current statistic from those maintained sums.

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.

\[\mu^x_t,\mu^y_t,\sigma^2_{x,t},\sigma^2_{y,t},c_{xy,t} = \operatorname{rollstats}(x_t,y_t,n)\]

\[\rho_t=\frac{c_{xy,t}}{\sigma_{x,t}\sigma_{y,t}}, \qquad \beta_t=\frac{c_{xy,t}}{\sigma^2_{x,t}}\]

The return value is the current scalar indicator value.

Implementation Notes

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

Reference

Background reference