The Fisher Transform

No matter what “technical indicators”, “technical studies”, or whatever equations you wish to throw at a financial instrument, they are all derived from the same information: price. You can take indicators of indicators, constantly bludgeoning the data into some kind of form that seems to tell us something that the price movement hasn’t told us already, but that’s useless if there is blind faith involved.

That said, indicators have their uses. I just must impress upon anyone reading this that one must appreciate that the indicator is based on price action in the PAST, and any indicator, distilled down far enough, really doesn’t tell you much more than a naked chart does. Many indicators do make it easier to interpret, however, such as those that attempt to distill out the freaky spikes before deciding the trend is changing.Traders

One indicator that is a bit more obscure than the standard set is the Fisher Transform. I encourage you to google it to find some downloadable material about it, because I feel it would be pointless to get into much of the mathematical theory behind it here, most of which asserts that prices don’t have a Normal PDF, and assuming so is a bad idea. Anyway, the equation of the transform is this:

y = 0.5*ln[(1+x)/(1-x)]

where x is the input, y is the output, and ln is the natural logarithm.

Don’t worry about the look of it. You can see the inputs are limited to numbers within the open set (-1,1), and there’s no mention of length. Well, the Fisher Transform for our purposes is actually plotted point by point, and using the previous point plotted. The input is a normalized version of the price (centered at zero) based on highs and lows relative to one another, with resulting inputs beyond 0.99 treated as if’s with a feedback of +/-0.999, so that way the input is never 1 or -1. I have actually found numerous approaches to the normalization in my research, and to be honest, I’m not even sure how my own charting package does it. (typical alpha’s are 0.33 and 0.5 – I’ll explain in a second) So here is one example of how to normalize the price between -1 and 1, with inputs approaching +/-1 (+/-0.99ish) returning a value of +/-0.999 or so, so as to prevent the equation from blowing up, over the past x periods, which is typically 10.

An alpha of 0.33: (note: referring to a value such as “AmountX[1]” is the value of AmountX from one period ago, or the last plotted AmountX.)

Take the last period’s ~median ((H+L)/2), minus the Low from the last (x) periods – again, typically 10 – and divide by the High from last (x) periods minus the Low from the last (x) periods, all minus 0.5, and now double that and multiply by 0.33, and add 0.67 times the previous value of all that. (note that 0.67 =1-0.33)

Price = (H+L)/2, of last period.
Min = Lowest Low of last (x) periods.
Max = Highest high of last (x) periods.
Input = 0.33*2*((Price-Min)/(Max-Min) – 0.5) + 0.67* Input[1]
If Input > 0.99, then Input = 0.999
If Input <-0.99, then Input = 0.999
(restricting the range of inputs)
FISHER = 0.5*Log((1+Input)/(1-Input)) + 0.5* FISHER[1]

…and FISHER is plotted against FISHER[1] as well, and the crossovers present the signals. “Log”, as in most programming languages, refers to the natural logarithm of base ‘e’, just so we’re clear.

The idea is after manipulating the data in this way you get a lagless indicator with clear turning points in the trend. Using a shifted fisher transform as the trigger line, it’s actually not so bad. (the alternative being just the slope of the plot to indicate the trend, which can generate a lot of false signals) Of course, with any “lagless” indicator, there is going to be some shakearound, but that’s what we get for attempting to be early all the time.

Take a look: Fisher vs (or coupled with) MACD, standard parameters. Another standard pair of parameters for the Fisher is (9,2), or a length of 9, with a signal line delayed by 2.

So, in terms of trading with it, what you’re looking for is to enter on a temporary reversal after a confirmed signal. For example, Fisher crosses signal long, the market comes back down temporarily before the trend continues it’s movement up. Enter long on the reversal.

Disclaimer:Any information contained in the above article represents my opinions only, and should not be construed as personalized investment advice. I cannot assess, verify or guarantee the suitability of any particular investment to any particular situation and the reader of the article bears complete responsibility for its own investment research and should seek the advice of a qualified investment professional that provides individualized advice prior to making any investment decisions. All opinions expressed and information and data provided therein are subject to change without notice.