The Ehlers filters: treating price as a signal

John F. Ehlers is an engineer who spent years applying digital signal processing — the mathematics of extracting a signal from noise — to market data, across several books and a long run of articles in Stocks & Commodities. If you have met the Relative Vigor Index on the previous pages, you have already met his work: that one is his too.

The premise

Treat a price series as a signal arriving over time. Inside it there is something you want — the underlying movement — and something you do not: the jitter of individual transactions, spread noise, one-off prints. Separating those is a problem engineers have worked on for a century, and they have much better tools for it than «average the last twenty».

His criticism of the simple moving average is technical and specific. It is a filter, and judged as a filter it behaves poorly: it does not suppress the frequencies it is supposed to suppress cleanly, and some of them come through inverted. In plainer terms, part of the noise you were trying to remove is still in the output, and part of it is now pushing the line the wrong way. That is not a matter of opinion; it is what the arithmetic of a boxcar average does.

The Super Smoother

His answer to that is a filter borrowed from electronics, designed so that the frequencies you want to remove are genuinely removed and the ones you want kept pass through with as little delay as the mathematics permits.

The practical claim is narrow and, unusually for this field, testable: for a given amount of smoothing it produces less lag than the moving average that smooths equally. Not zero lag — less. The trade-off described on the first page of this section still applies; it is simply a better position on the same curve.

The Fisher Transform

A different kind of idea, and the one most worth understanding because the reasoning transfers.

Price, rescaled into a band, tends to spend its time spread fairly evenly across that band — there is no strong pull to the middle. That is awkward if what you want to identify is an extreme, because in a roughly even spread nothing is very extreme.

The Fisher Transform applies a mathematical reshaping — the inverse hyperbolic tangent, if you want the name — that stretches the ends of the range and compresses the middle. After it, middling readings all look similar and genuinely unusual readings stand sharply apart, which is exactly the property you wanted from an oscillator and rarely get.

Worth being precise about what happened there. The transform did not find anything new. It redistributed what was already present so that a threshold means something more consistent. That is a real improvement in a real weakness — and it is presentation, not new evidence.

MESA and the adaptive average

The most ambitious of his ideas, and the one to approach with the most care.

Every indicator on every page of this section needs a period: fourteen bars, twenty bars. That number is a guess about the timescale the market is currently operating on, and it is fixed while the market is not. Ehlers' proposal: measure the dominant cycle in the data and set the period from the measurement. The technique he borrowed for the measuring — maximum entropy spectral analysis, which is where MESA comes from — came out of geophysics, where it was used to extract periodicity from short, noisy records. The resulting adaptive average speeds up when the market's rhythm shortens and slows down when it lengthens.

The idea is genuinely clever and it rests on a premise that has to be stated as a premise: that a dominant cycle is there to be found. Sometimes one is. In a directional market there is no cycle, only trend, and a cycle-measuring instrument asked for a period under those conditions will still return one. Ehlers is explicit about this himself and distinguishes trend conditions from cycle conditions, which is more than most authors do about their own tools. It is repeated here because a reader meeting the adaptive average second-hand will usually not be told.

What the filters do not do

This is the section that keeps the page honest, and it applies to every tool above.

A better filter gives you a better filter. It does not widen the input. Every one of these is still computed from the same open, high, low and close as the twenty-period average it improves on — so it cannot know about resting size, who crossed the spread, or anything that has not traded yet.

Which is worth knowing in both directions, because the conclusion is not «ignore this». The conclusion is that these belong to a particular kind of problem: you have decided to smooth something, and you would like to pay less for it. On that problem the engineering is real and the improvement is measurable. On the question of what is happening in the market right now, they are as blind as the average they replace — which is what the order book and the tape are for, and why they sit in a different part of this path.