GaussianProcessRegressionBands

Summary

GaussianProcessRegressionBands is RTTA's streaming implementation of: Rolling RBF-kernel Gaussian process posterior mean with uncertainty bands.

Update API

result = rtta.GaussianProcessRegressionBands(window=16).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

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

\[K_{ij}=k(x_i,x_j)+\sigma^2\delta_{ij}\]

\[\mu_t=k_t^\top K^{-1}y, \qquad \sigma_t^2=k(z_t,z_t)-k_t^\top K^{-1}k_t\]

update(...) returns a result struct with fields middle, upper, lower.

Implementation Notes

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

Reference

Background reference