Variance - RTTA

Summary

Variance is RTTA's streaming implementation of: Rolling variance.

Update API

result = rtta.Variance().update(value)

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

Theory Of Operation

Variance keeps centered rolling sufficient statistics. Each update inserts the newest sample, removes any expired sample, and rebases the centered moments when the rolling anchor changes.

Recurrence

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

\[\mu_t=\frac{1}{|W_t|}\sum_{i\in W_t}x_i\]

\[\sigma_t^2=\frac{1}{|W_t|}\sum_{i\in W_t}(x_i-\mu_t)^2\]

The return value is the current scalar indicator value.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class Variance. It evaluates variance from differences to a rolling anchor instead of the cancellation-prone identity \(E[x^2]-E[x]^2\). This remains accurate when, for example, prices near \(10^7\) move by only a few cents.

Reference

Background reference