BollingerBands

Summary

BollingerBands is RTTA's streaming implementation of: Moving-average envelope based on standard deviations.

Update API

result = rtta.BollingerBands().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

BollingerBands combines a rolling mean with a rolling population-standard- deviation envelope. The middle band is the local mean, while the upper and lower bands mark a two-standard-deviation channel around it.

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.

\[M_t=\operatorname{SMA}_n(x_t), \qquad S_t=\operatorname{StdDev}_n(x_t)\]

\[upper_t=M_t+2S_t, \qquad lower_t=M_t-2S_t\]

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

Composed Primitives

SMA, StdDev

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class BollingerBands. Mean and variance share centered rolling moments, avoiding cancellation at large absolute price levels.

Reference

Background reference