Cascades
Build something smooth and hopelessly late, then subtract a deeper copy of it. What is left is most of the smoothness without most of the lateness, and there is a dial that runs all the way to no lateness at all.
Build one
Lag, noise gain, peak gain and leak are defined on the comparison page — the tool sits above the article deliberately, so the numbers arrive before the prose that explains them.
How it works
Chain a few exponential averages together and the result is beautifully smooth and unusably slow. But the lag they add is regular, and regular things can be subtracted.
The generalised construction is one line. Write E for one exponential average, and GD(x) = (1 + v)·E(x) − v·E(E(x)).
At v = 0 this is just E. At v = 1 it is 2E − E², which is DEMA. Apply GD three times with v = 0.7 and you have Tillson's T3, published in 1998. The coefficients that fall out sum to exactly one, always — worth knowing, because it means the construction needs no normalisation and any implementation that needs one has a bug.
Hull and the zero-lag EMA are the same idea with different levers. Hull differences two weighted averages of different spans and smooths the result. ZLEMA does not touch the filter at all: it feeds an ordinary exponential average 2·price − price[half a span ago], a first-order guess at where price was heading.
What it costs
Here is the part the genre does not print. The dial from very late to not late at all is real, it works, and every step of it is paid for:
What our measurements say
And the family beside the rest of the table:
| Filter | Lag | Noise | Peak | Leak | vs an EMA of the same lag |
|---|---|---|---|---|---|
| Hull | 0.67 | 0.1792 | 1.287 | 0.04552 | leak 0.0817× · noise 0.418× |
| ZLEMA | 0.50 | 0.1417 | 1.145 | 0.14882 | leak 0.235× · noise 0.283× |
| T3 (v=0.7) | 10.35 | 0.0420 | 1.135 | 0.00095 | leak 0.0146× · noise 0.911× |
Within this family the shortest lag here is ZLEMA at 0.50 bars and the least leak is T3 (v=0.7) at 0.00095, and they are not the same filter: ZLEMA leaks 0.14882 to buy that speed, and T3 (v=0.7) sits 10.35 bars back to buy that quiet. Leak is measured over periods of 4.0 bars and shorter, the same band as every other page in this section, so the rows can be read against the full table.
Overshoot is not noise
The peak gain column is the one to watch here, and it is a different complaint from noise. Noise gain says random movement comes out larger. Peak gain says that at one particular frequency the filter systematically magnifies, so after a real move the line carries past the price and hangs there — on every instrument, every time, not on average.
A line that leads price is not seeing the future. It is overshooting, and it will overshoot the reversal too.
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.
- 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.
- Adaptive — Re-estimate the period every bar. The one construction with no fixed response, which is why it is absent from the table above.
- All of them on one ruler — the comparison this page is part of.