Filter Lag in Engineering Terms
How does filter delay shift the time at which a trading signal becomes usable?
For an n-period simple moving average, the low-frequency group delay is (n-1)/2 bars under its linear-filter model. Align signal and fill timestamps before comparing indicators; a smoother curve can reflect added delay rather than improved prediction.
An N-period simple moving average has low-frequency group delay (N-1)/2 bars; matched-lag comparison is methodological advice.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | Ehlers's treatment of technical indicators as digital filters, which is what they are. |
| Key result / formula | Each smoothing indicator is a filter with a frequency response: it passes slow components of the series and attenuates fast ones, and the degree of attenuation is set by the weights. |
| Why it matters for backtesting | The filter view is worth having because it makes two things precise that users argue about. |
What it is
Once a moving average is seen as a low-pass filter, its lag, its frequency response and the trade-off between smoothing and delay become computable rather than matters of preference.
Key result / formula
Two quantities follow. The lag is the delay a filter imposes on a signal passing through it, and for a simple average it is (n-1)/2 bars at low frequency for an n-period simple moving average, which is why a long average reacts so late. The smoothing is the attenuation of high-frequency content, which is what makes the line look clean. The two are linked: within a family, reducing lag costs smoothing and vice versa, and no choice of weights escapes the trade-off entirely, though some weightings are better than others at a given lag. Ehlers designs filters aimed at improving that trade-off and treats the market series as containing cycles whose periods can be estimated and tracked, which is the more speculative part of his program.
Why it matters for backtesting
A crossover system's behaviour is largely determined by the lag of its components, so a comparison between two systems with different lags is not a comparison of ideas, and matching lag before comparing is the sound procedure. And the visual appeal of a smooth indicator is bought with delay, which is a cost paid in entries, so the choice should be made on measured performance. The cycle-estimation half of the program deserves a warning from elsewhere in the pack: a smoothed series of noise displays cycles with no cyclical cause (see [Slutsky Effect: A Moving Average of Noise Manufactures Cycles]), so an estimated period must be tested against a null that has none.
Source
Ehlers, Cycle Analytics for Traders: Advanced Technical Trading Concepts, Wiley, 2013. Primary source