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RainbowMovingAverage

Incremental, causal technical analysis documentation

Summary

RainbowMovingAverage is RTTA's streaming implementation of Mel Widner's rainbow: a stack of recursive simple moving averages. Each layer is an SMA of the previous layer. The indicator returns the deepest layer, the envelope of all layers, and the rainbow width.

Update API

result = rtta.RainbowMovingAverage(period=2, layers=10, fillna=True).update(price)
# result.outer, result.highest, result.lowest, result.mid, result.width

The update(...) call consumes one price observation. advance(...) uses the same input when the caller wants to update state without materializing a Python return value. Array batch(...) / replay_update_outputs(...) follow the same multi-output path as other RTTA result structs.

Theory Of Operation

Widner's rainbow builds a family of nested smoothers rather than a single MA. Layer \(1\) is an SMA of price; layer \(k\) is an SMA of layer \(k-1\). Deeper layers lag more, so the set of layers fans out when price trends and collapses when price consolidates. RTTA keeps one causal SMA state per layer and, each tick, feeds the previous layer's output into the next.

Recurrence

Let \(x_t\) be the input price, \(p\) be period, and \(L\) be layers.

\[S^{(1)}_t = \operatorname{SMA}_p(x_t), \qquad S^{(k)}_t = \operatorname{SMA}_p\!\bigl(S^{(k-1)}_t\bigr) \quad\text{for }k=2,\ldots,L\]
\[H_t = \max_{1\le k\le L} S^{(k)}_t, \qquad L_t = \min_{1\le k\le L} S^{(k)}_t\]
\[\begin{aligned} \operatorname{outer}_t &= S^{(L)}_t \\ \operatorname{mid}_t &= \tfrac12(H_t + L_t) \\ \operatorname{width}_t &= H_t - L_t \end{aligned}\]

With fillna=False, outputs are NaN until roughly \(p\cdot L\) samples have been seen (each successive SMA adds lag). With fillna=True, partial SMA means are emitted during warmup.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class RainbowMovingAverage. Each layer is a nested SMA member; the result struct fields are outer, highest, lowest, mid, and width.

Reference