NadarayaWatsonEnvelope

Summary

NadarayaWatsonEnvelope is RTTA's streaming implementation of: Gaussian-kernel Nadaraya-Watson smoother with weighted residual bands.

Update API

result = rtta.NadarayaWatsonEnvelope(window=32).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

NadarayaWatsonEnvelope is a causal smoother or average. It updates compact rolling or exponential state with the newest observation and returns the current smoothed estimate.

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.

\[w_{t,i}=\exp\left(-\frac{(t-i)^2}{2h^2}\right)\]

\[\hat{x}_t=\frac{\sum_{i\in W_t}w_{t,i}x_i}{\sum_{i\in W_t}w_{t,i}}\]

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

Implementation Notes

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

Reference

Background reference