Constructing RSI on highs, lows, and reverse targets

The 0-100 ratio

The relative-strength-index of an arbitrary series is a 0-100 ratio of a smoothed up-change series to the sum of that series and a smoothed down-change series.

An up-change equals the period-to-period rise in the series when that rise is positive and equals zero otherwise. A down-change equals the period-to-period fall when that fall is positive and equals zero otherwise. Those smoothed series are the average-up and the average-down.

Smoothing with a wilder-lookback

When the RSI lookback is k periods, the up-change and down-change series are each smoothed with a (2k-1)-period exponential moving average. The wilder-lookback is that period count k. It sets the exponential smoother length at twice k minus one.

Worked implementations use a default wilder-lookback of 14 and set the exponential length to twice that lookback minus one.

The 0-100 RSI ratio is formed with a tiny positive addend in both the numerator and the denominator so a zero pair of average-up and average-down values does not divide by zero.

Highs, lows, and closes

Substituting highs or lows for the chosen series yields high-based-rsi and low-based-rsi readings together with matching reverse-engineered companions.

Substituting closing prices for the chosen series recovers the classic close-based RSI and its reverse-engineered counterpart.

A reverse-engineered next value

Reverse-engineered-rsi converts a chosen projected-rsi reading into the next value of the series from the prior series value and a signed increment that is scaled differently when that increment is negative.

Reverse-engineered implementations take a target RSI reading, defaulting to 50 and bounded from 1 to 100, plus the wilder-lookback.