Adaptive
Estimate the market's dominant period every bar and retune the filter to it. It is the most appealing idea in this section and the only one with no generator on its page, because we measured the thing it rests on.
How it works
The recipe is always the same. Detrend the price, estimate where its energy sits — by spectrum, or by looking for the lag at which the series most disagrees with itself — call the result the dominant cycle, and set the filter's period to it.
Notice that this construction has no fixed impulse response. Its coefficients change every bar, so the four numbers every other page here prints cannot be computed for it at all. That is not a technicality. It is why adaptive indicators are presented with pictures rather than with measurements.
What it costs
An adaptive period is only worth having if two things are true. There has to be a peak in the spectrum that is not there by chance, and that peak has to stay put long enough to adapt to. Both are testable without writing a single indicator, and they are separate questions from whether volatility has a cycle, which it does.
What our measurements say
So we tested them. First the spectrum itself, against a null of the same returns, shuffled. Shuffling destroys every serial dependence and leaves the fat tails untouched, so a peak that survives it is structure and not kurtosis. Two hundred shuffles for the band.
In the returns, nothing stood up. Across three majors on hourly bars, no bin anywhere reached 1.2× the 99th percentile of the shuffled band; about ten bins per instrument cleared the band at all, which is what a thousand bins and a 99% band produce by chance, and the bins that cleared it repeated on no second instrument. The period estimated on one window did not predict the next: six instrument-estimator cells, every one within ±1.6 standard deviations of shuffled.
In the absolute returns, a peak stood up enormously — 24 bars at six to twenty-nine times the band, on all three, and again at 98 bars on M15 and 293 on M5. That is the trading day at each scale, and it is the most useful result here for two opposite reasons. It is real, so the null above is not the method failing to see anything: fed a cycle, these estimators find it and find it loudly. And it is a volatility clock rather than a cycle in price, already priced by an ATR-by-hour table, and not a period an indicator's lookback can be set to.
Then the claim at the level it is actually made: does setting an indicator's lookback from the measured cycle beat leaving it constant? Three majors, hourly bars, 2000 to 2026, about ten thousand events per arm.
| Arm | Reached +2 ATR |
|---|---|
| Adaptive, Welch estimator | 33% [33–34] |
| The same periods, shuffled | 34% [33–35] |
| Adaptive, Burg estimator | 34% [33–35] |
| Fixed N = 10 / 20 / 40 / 80 | 34% / 33% / 33% / 34% |
The shuffled arm is the one that matters. It uses the same periods the adaptive arm produced, in a permuted order: same distribution, same clamps, same machinery, each period attached to the wrong bar. The adaptive arm does not beat it. Whatever the spectrum contributed, it was not information about which bar it was attached to.
What this does and does not settle
We tested our own setting: a channel breakout whose only parameter is the lookback, chosen because a second free parameter would let either arm win by tuning rather than by adapting. That is not a refutation of every adaptive scheme, and it is not a claim about band-pass filters tuned for mean reversion, which ask something different of the same estimate.
What it does settle is the premise underneath all of them, in one honest form: on hourly returns of the major pairs, over twenty-six years, there was no cycle in price to adapt to — nothing above chance, and nothing that held from one window to the next. There is a loud cycle in volatility, and it is the trading day. If your construction depends on the first, that is the thing to test first, and a shuffled control is what makes the test mean anything.
The other constructions
- Windows — Choose a shape, normalise it, and the shape is the filter.
- Poles — Place the poles of a recursion and let it run.
- Cascades — Build something smooth and late, then subtract a deeper copy of it to cancel the lateness.
- Laguerre — One exponential average, then all-pass sections that only delay, recombined.
- Least squares — State the response you want, including the delay, and solve for it.
- All of them on one ruler — the comparison this page is part of.