EndPointFFT

Background

The End Point Fast Fourier Transform (EPFFT) is a noise-filtered FFT rebuilt so it can actually be traded in real time. At each bar it transforms a trailing window of price, strips out the weak frequencies as noise, and keeps a single value — the end point. Stringing those end points together gives a smooth curve whose trend and, especially, whose turning points are what you watch. Because each value is locked in once and never revised in hindsight, the curve is honest about what you would actually have seen as each bar formed.

It comes from the published work of Dennis Meyers (his End Point Fast Fourier Transform articles in Stocks & Commodities). Keeping every surviving frequency, rather than just the single dominant cycle, makes it a more robust noise filter than a one-cycle method.

The FFT illusion

Why not just run an FFT across the whole chart? Because it will lie to you about the past. If you fit a noise-filtered FFT over an entire history, the curve hugs every top and bottom beautifully and can even seem to roll over just before a big decline, as if it predicted it. But that curve was drawn already knowing where the tops and bottoms were — the FFT's maths force a glove-tight fit to the data it is given. Re-draw it as it would have looked on the day of the top, using only the data available up to that day, and the apparent foresight evaporates: it points straight up into the drop. The smooth, prescient-looking whole-history FFT is hindsight, not prediction.

How the indicator works

To get an honest curve, the indicator walks forward one bar at a time. At each bar it noise-filters the FFT of the trailing window but keeps only the last point — the one value it could legitimately have known at that moment. Joining those end points reproduces what you would really have seen live. The honest cost is lag: instead of leading the turns, the EPFFT follows them by anywhere from zero to a few bars.

Each bar's value is built like this: take the natural log of the window (so a strong exponential trend does not dominate), remove its average level and straight-line trend, FFT it, zero out every frequency weaker than your Threshold times the strongest one, invert the transform and undo the log, then accumulate the change at the end point into a running curve. That running-sum construction keeps the curve smooth as the window slides forward and the raw numbers jitter.

Included formula

The toolbox ships a ready-made End Point FFT indicator, so you can see the curve without writing any code. In AmiBroker open the Charts window, expand the WiseTraderToolbox group and drag End Point FFT onto a chart; it plots the filtered curve, with the window length and noise threshold set from its parameters.

The band-breakout trading system described below is not part of that chart — the code here shows how to add it yourself.

The exported function

At the heart of the indicator is a single exported AFL function you can call directly. The rest of this page shows how to plot it and build a system around it.

Returns a per-bar array holding the end-point FFT curve.

Plotting the curve

// 64-bar FFT window, drop any cycle weaker than 20% of the strongest.
signal = EndPointFFT( Close, 64, 0.2 );
Plot( signal, "End Point FFT", colorBlue );

The trading system

Meyers traded the EPFFT curve exactly the way he traded the Goertzel curve: a stop-and-reverse band breakout that ignores the curve's small wiggles. You stay in the market and flip side only on a decisive turn — go long once the curve has rallied a set amount above the lowest point it reached while you were short, and go short once it has dropped a set amount below the highest point it reached while you were long. The runnable system on the Goertzel page drops straight onto this curve — just swap the Goertzel(…) call for EndPointFFT(…):

curve = EndPointFFT( Close, 64, 0.2 );   // then apply the same band-breakout rules

As with Goertzel, his intraday version also closed positions before the session ended and ignored the first hour of trading, and the two band sizes were fitted with walk-forward optimisation — tuned on one block of history and then traded on the untouched block that follows.