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10.15 Fisher Transform

The fisher transform indicator by John Ehlers is a range oscillator showing where today’s price is within the past N-days highest and lowest. It has some smoothing, plus what’s known in mathematics as a fisher transform.

The range position is similar to Stochastics and to Williams %R (see Williams %R). The fisher transformation stretches out values near the N-day high and low to make large peaks so as to help highlight those extremes.

The calculation is as follows. The prices used are the midpoint between the day’s high and low (as in most of Ehlers’ indicators). Today’s price is located within the highest and lowest of those midpoints from the past N days, scaled to -1 for the low and 1 for the high.

price = (high + low) / 2

            price - Ndaylow
raw = 2 * ------------------ - 1
          Ndayhigh - Ndaylow

This raw position is smoothed by a 5-day EMA (see Exponential Moving Average) then a log form which is the fisher transform, before a final further 3-day EMA smoothing.

smoothed = EMA[5] of raw

                       1 + smoothed
fisher = EMA[3] of log ------------
                       1 - smoothed

The effect of the logarithm is to make “smoothed” values near 0 remain near there, but values near 1 and -1 grow greatly, thus highlighting extremities. A “smoothed” value of exactly +/-1 would transform to +/-infinity, so a clamp of 0.999 is applied, effectively limiting the final result to about +/-7.5.

10.15.1 Additional Resources

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