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http://www.mesasoftware.com/technicalpapers.htm http://www.mesasoftware.com/Papers/USING%20THE%20FISHER%20TRANSFORM.pdf

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*.

- http://www.linnsoft.com/tour/techind/fish.htm – sample Nasdaq 100
symbol ‘
`QQQ`’ from August 2002. (For Chart use Yahoo symbol ‘`^IXIC`’ to get that data).

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