2016issue C0910-15
Tuning indicators to measured market cycles
Treat indicator lookbacks as measured cycle periods rather than inherited defaults. Judge each measurement method by how it handles noise, changing periods, and spectral dilation before any adaptive tuning is applied.
- Indicator lookbacks can be taken from measured cycle periods in the data rather than from a fixed conventional default.
- A cycle estimator should be judged by noise, changing periods, and spectral dilation before any adaptive tuning is applied.
- An autocorrelation periodogram strips spectral dilation by transforming normalized lagged self-comparisons, then estimates relative cycle amplitudes.
- MESA extracts high-resolution cycle estimates from short, locally stable samples by tuning a filter and reading that filter offline.
Lookbacks as measured periods
Indicator lookbacks can be chosen from measured cycle periods in the data rather than from a fixed conventional default such as a common RSI length. The dominant cycle is the cycle period with the greatest usable spectral amplitude in a defined lookback window. Spectral analysis is the estimation of cyclic component periods and relative amplitudes from ordered market observations.
Why cycle measurement is hard
Market cycles are hard to measure because they appear and disappear, their periods change, the data are noisy, and swing amplitude scales with period. Spectral dilation is that tendency of swing amplitude to grow with cycle period, which can bias naive period estimates toward longer cycles.
How to judge a measurement method
Bar-to-bar phase methods infer period from instantaneous phase shift, but they fail when the data are noisy. Longer averaging improves signal-to-noise, yet several digital signal processing estimators still fail. Some do not converge when periods change, and short-window Fourier or wavelet estimates have poor resolution. None of those listed methods correct spectral dilation.
Autocorrelation periodogram
An autocorrelation test is a lagged self-comparison of filtered data whose Fourier transform yields a periodogram of cycle content. An autocorrelation periodogram first autocorrelates the series. Those correlations are normalized and bounded, which strips spectral dilation while keeping periodicity. A Fourier transform of the autocorrelation then estimates relative cycle amplitudes without that bias.
Maximum entropy spectral analysis
MESA, or maximum entropy spectral analysis, tunes a short-segment filter so residual noise is maximized, then inspects that filter offline. The method allows high-resolution cycle estimates from short, locally stable samples and extracts cyclic response independently of data length.
A roofed measurement workflow
A roofing filter is a high-pass plus SuperSmoother pair that limits the band of data before cycle measurement. The supplied implementation roofs the series, computes Pearson correlations across a range of lags, forms a periodogram over a matching band of periods, optionally emphasizes stronger peaks in normalized power, and takes the spectrum center of gravity as the dominant cycle when peak power meets a minimum threshold.
What a historical comparison showed
In a historical comparison under matching sample blocks, an autocorrelation periodogram showed dominant periods that changed more than once, a stretch with no useful cycle because the spectrum was smeared, a shorter reading after a sharp drop, and later a return to a usable reading. MESA on the same conditions produced thinner, higher-resolution spectral lines and a component present most of the time, with longer cycles also visible in some stretches.
All readings on this track · 15 readings
- 1987Evaluating weekly price cycles with autocorrelation cutoffs
- 1988Serial correlation is not an independence test
- 1988Event-triggered chi-square tests for jittered serial links
- 1988Reverse the rule before you trust the system
- 1990Chi-square evaluation of lagged breadth correlations
- 1990Two-gate out-of-sample tests for trading rules
- 1990Sign-cell correlation, chi-square checks, and lag shifts
- 1998Test serial dependence before you optimize a mechanical system
- 2003How a one-rank rotation is constructed for an offset autocorrelation check
- 2004Constructing first-order residual autocorrelation tests
- 2004A two-stage Durbin-Watson residual screen
- 2011Constructing trend labels from increment correlation atoms
- 2012Overnight versus daytime return evaluation
- 2012Constructing a multi-horizon folded-correlation reversal filter
- 2016Tuning indicators to measured market cycles