ArnaudLegouxMovingAverage

Summary

ArnaudLegouxMovingAverage is RTTA's streaming implementation of: Arnaud Legoux moving average with Gaussian weights controlled by offset and sigma.

Update API

result = rtta.ArnaudLegouxMovingAverage().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

ArnaudLegouxMovingAverage applies a fixed Gaussian window to the most recent window samples. The peak of the Gaussian is placed at offset * (window - 1) from the oldest sample, so larger offset values put more weight on recent prices. sigma controls how peaked the kernel is.

Recurrence

Let \(z_t = value_t\) denote the observation consumed by one update(...) call, \(n\) the window length, \(o\) the offset, and \(s=n/\sigma\).

\[m = o(n-1), \qquad w_i = \exp\!\left(-\frac{(i-m)^2}{2s^2}\right), \quad i=0,\ldots,n-1\]

\[y_t = \frac{\sum_{i=0}^{n-1} w_i z_{t-n+1+i}}{\sum_{i=0}^{n-1} w_i}\]

Index \(i=0\) is the oldest sample in the window and \(i=n-1\) is the newest. Until the window is full, only the available samples and their matching weights are used when fillna=True.

The return value is the current scalar indicator value.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class ArnaudLegouxMovingAverage. Weights are precomputed in the constructor.

Reference

Background reference