> *Mel Widner applied SMA ten times recursively, then weighted the layers like a rainbow: brightest at the top, fading toward the base. Ten colors of smoothing, one composite average that sees both fast and slow structure simultaneously.*
- RAIN recursively applies SMA 10 times, producing 10 layers of progressively smoother price representation, then computes a weighted average across ...
RAIN recursively applies SMA 10 times, producing 10 layers of progressively smoother price representation, then computes a weighted average across all layers. Layers 1-4 receive weights 5, 4, 3, 2 (emphasizing the more responsive layers), while layers 5-10 each receive weight 1, for a total divisor of 20. This multi-scale composition produces a moving average that responds to short-term price changes through the lightly smoothed upper layers while maintaining stability through the heavily smoothed lower layers.
## Historical Context
Mel Widner published "Rainbow Charts" in *Technical Analysis of Stocks & Commodities* (1998), introducing the concept of recursive SMA application as both a visualization technique and a composite smoothing method. The thinkorswim platform later standardized the weight vector as $[5, 4, 3, 2, 1, 1, 1, 1, 1, 1]$, which became the canonical RAIN MA.
The recursive SMA application has a deep mathematical interpretation: applying SMA $k$ times is equivalent to convolving the rectangular kernel with itself $k$ times, which produces a B-spline kernel of order $k$. Thus RAIN's 10 layers correspond to B-splines of orders 1 through 10, and the weighted average blends these spline approximations. The B-spline interpretation explains why higher layers are smoother: each convolution adds a degree of polynomial reproduction and reduces the spectral sidelobe level.
The weight vector $[5, 4, 3, 2, 1, 1, 1, 1, 1, 1]$ with sum 20 was chosen empirically rather than derived from optimization theory. The declining weights for layers 1-4 bias the output toward the more responsive layers, making RAIN track trends more closely than a uniform average of all 10 layers would.
## Architecture & Physics
### 1. Ten Cascaded SMA Layers
Each layer is an SMA applied to the previous layer's output:
Each of the 10 SMA layers uses a circular buffer with a running sum, giving O(1) per-bar update cost per layer. Total cost: O(10) per bar, with O($10 \times N$) memory for the 10 buffers.
- Widner, M. (1998). "Rainbow Charts." *Technical Analysis of Stocks & Commodities*.
- thinkorswim / TD Ameritrade. "RainbowAverage" study documentation.
- Schoenberg, I.J. (1946). "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions." *Quarterly of Applied Mathematics*, 4(1), 45-99. (B-spline theory underlying recursive SMA.)
RAIN(N) composes 10 independent SMA(N) instances in parallel. Each SMA uses O(1) running-sum via its ring buffer. The composite output is a weighted sum of the 10 SMA results — all computed from the same input value.
O(1) per bar. Each of the 10 SMA layers is O(1); the composite sum is 10 FMA operations. WarmupPeriod = period × 10 (all layers must reach steady state).
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| 10 independent SMA running sums | Yes | All 10 sums independent per bar; `VADDPD` on 10-channel register set |
| 10 SMA divides | Yes | 10 `VDIVPD` ops; can be vectorized as 10-wide FP array |
Because all 10 SMA layers are independent, the entire computation can be vectorized across layers AND across bars simultaneously. AVX2 can process 4 bars per pass, each bar updating all 10 layers via 10-register prefix sums. Estimated batch speedup for large series: ~6× over scalar.
