Zero-lag cycle filters can fail on a price series

A filter bank, not an entry rule

The source treats market prices as a noisy stream that can be scanned with a bank of resonators, each tuned to a slightly different period, until one band responds as a coherent cycle rather than as random stimulation. That strongest recurring rhythm is the dominant cycle a detector reports in a price, volume, or breadth series over a defined lookback.

The intended teaching object is not an extra entry rule but a zero-lag filter bank, analogous to tuned circuits, whose bandwidth and overlap can be adjusted to isolate non-seasonal market rhythms. A zero-lag filter keeps the extracted cycle in phase with the original series rather than delayed like a moving average.

The lowpass stage fails a constant-input check

The published lowpass stage fails a basic constant-input check. A lowpass-filter is meant to pass slow components, including a near-constant level, while rejecting high-frequency noise. On a steady series the output does not settle at the same level as the input. The mismatch is most visible on series with large level, such as an S&P 500 close in the 700s.

That large near-constant level is the dc-offset. Recursive filters can mishandle it even when the frequency plot still looks orderly.

Roundoff and design fitness

One identified cause is single-precision recursive arithmetic. Small roundoff errors accumulate when the series has a large dc-offset, while relatively centered data can still behave as designed.

A second cause is the filter's own design fitness. The genetic search favored impulse and frequency shape under coarse bar spacing and paid little attention to gain and offset. Those gaps only became acceptable because the lowpass-filter was meant to sit inside a bandpass-filter with a high-pass companion. A bandpass-filter passes a chosen band of cycle lengths and attenuates slower drift and faster noise.

When the offset can be left alone

The correction note states that those offsets may be tolerable when the only concern is phase and frequency response inside a bandpass-filter, but they need compensation if the lowpass-filter is used on its own.

TradersWeek editorial view: treat the frequency chart as a shape check, not as proof that the same lowpass-filter is a usable standalone signal on a raw price series.