Building a bounded oscillator from a rainbow smoother, relative strength, and inverse Fisher

Four stacked transforms

The construction assembles a bounded oscillator from four successive transforms. A moving average first replaces raw closes with a rainbow-smoothed series. A relative-strength index is then computed on that series. A zero-lag exponential moving average is applied to a recentered form of that oscillator. An inverse Fisher map, followed by a linear rescale, places the finished series on a 0-100 scale.

Here a relative-strength index is a bounded oscillator of average up versus down changes over a stated lookback, applied to a rainbow-smoothed price series rather than raw closes. A moving average is a weighted or exponential average of ordered prices or intermediate series. In this pipeline it is used both as the rainbow pre-smoother and as the zero-lag exponential stage before the inverse Fisher map.

Rainbow weighted average of close

The first stage replaces raw closes with a rainbow weighted moving average. That average is built from nested two-bar weighted averages of close, then scaled by descending weights 5 through 1 plus five further nested terms, all divided by 20.

Relative strength and a compact signed input

Relative strength is computed on that rainbow series over a default four-bar period. The oscillator is then recentered as 0.1 times the oscillator minus 50 so the next stage receives a compact signed input.

Zero-lag exponential correction

A two-pass exponential moving average of that recentered series, also defaulted to four bars, is combined as the first pass plus the difference of the two passes. The combination is the zero-lag exponential value passed to the map.

Inverse Fisher map and the 0-100 scale

The inverse Fisher map y = (exp(2x) - 1) / (exp(2x) + 1) is applied to the zero-lag value. The mapped series is then rescaled by adding 1 and multiplying by 50 so the finished series sits on a 0-100 scale.

Coded trigger levels and editable periods

In the supplied implementations, a cross of the transformed series above 12 and a cross below 88 are the coded long and short trigger levels. Those crossings are evaluated next bar at market in the strategy form.

The same pipeline is parameterized with separately editable RSI-period and EMA-period inputs, both defaulting to 4, so the construction can be rebuilt without changing the transform algebra.