1985issue C071-12
Constructing period-locked half-cycle and full-cycle averages
Both averaging windows are locked to a measured dominant period so the dual average is built from the series rather than taken from a default length. A short recent spectrum then judges whether leftover tones leave that construction unusable.
- A cycle reading is admissible only when an oscillation already exists in the historical series and is assumed to continue. A large external shock can overwhelm any technical cycle structure.
- A full-period average cancels a sine and leaves a flat line or the added linear drift. A half-cycle window yields a cosine-like companion delayed by a quarter cycle. On a pure sine, the constructed signal is their crossing.
- An assumed period that is half the true period leaves a cyclic residual in the long average and advances the crossovers. An assumed period twenty-five percent too long delays them. In-phase harmonics can still shift buys and sells when the period is known exactly.
- The two-window construction is treated as unusable when any secondary spectral component remains within about one-third the amplitude of the dominant cycle, a threshold stated as ten decibels. A short-lookback maximum entropy spectrum judges that leftover content.
Locking both windows to the dominant period
Editorial: TradersWeek treats the dual moving average as a built instrument rather than a chart habit. Both windows are locked to a measured dominant period, then a short-sample spectrum decides whether leftover tones make the construction inadmissible.
The dominant cycle is the strongest repeating period in a price, volume, or breadth series. Both averaging windows are set from this period rather than from a conventional default length.
A cycle reading is only admissible when an oscillation already exists in the historical series and is assumed to continue. A large external shock can overwhelm any technical cycle structure.
The half-cycle window and the full-period trendline
A moving average whose window equals one full sine period cancels the oscillation, leaving a flat line or, if a linear drift is added, that drift. The full-period average is therefore forced to act as a local trendline.
A half-cycle window is a moving average whose length is half the dominant period. On a sine it reconstructs a cosine-like companion delayed by a quarter cycle and is used as the fast leg.
On a synthesized pure sine, the constructed signal is the crossing of the half-period average through the full-period average. That crossing is the moving-average crossover: a buy or sell mark defined where the half-period average crosses the full-period average.
Period error and the phase-reversal test
Setting the assumed dominant period to half the true period leaves a strongly cyclic residual in the long average and advances the crossovers.
Setting the assumed dominant period twenty-five percent longer than the true period delays the same crossovers.
The dominant period can be estimated with a phase-reversal test, a manual search in which the long-window length is iterated until residual wiggles sit at the boundary between matching and opposing the original wave. In practice the longer average is iterated until those residual wiggles sit at the transition between matching and opposing the price wave.
Leftover tones and the short-sample spectrum
Spectral purity is how completely the series is dominated by a single tone. A pure sine has one sharp peak, while added harmonics smear the spectrum and shift the crossovers.
A sawtooth assembled from in-phase harmonics delays buys and advances sells even when the dominant period is known exactly.
The two-window construction is treated as unusable when any secondary spectral component remains within about one-third the amplitude of the dominant cycle, a threshold stated as ten decibels.
Maximum entropy spectrum analysis is used to judge that leftover content because a short recent sample keeps the estimate aligned with current data. Editorial: that short-lookback spectrum is the gate that decides whether the period-locked construction is admissible.
All readings on this track · 28 readings
- 1984Constructing maximum-entropy spectra for dominant-cycle forecasts
- 1984How to construct a maximum-entropy cycle model
- 1984Constructing a maximum-entropy forecast from a chosen lookback
- 1985Constructing period-locked half-cycle and full-cycle averages
- 1986Why Fourier windows limit dominant-cycle resolution
- 1987Assembling short-lookback maximum-entropy cycle forecasts
- 1988Why a fitted dominant cycle is not a forecast
- 1989Evaluating commodity cycle personalities with spectral histograms
- 1989Evaluating next-session cycle forecasts with stops
- 1989Constructing cycle-aged volatility trailing stops
- 1990A channel signal-to-noise gate for dominant-cycle forecasts
- 1990Year-over-year dominant cycle personality audit
- 1991Cyclic entry from a locked dominant-cycle phase
- 1992Stationarity states on synchronized futures spectral contours
- 1997Hidden horizon assumptions in dominant-cycle readings
- 1997When market cycles are absent more than present
- 1997A spectral estimator that retunes indicators to the measured cycle
- 2000Constructing a Hilbert dominant cycle and a maximum-entropy refinement
- 2000Switch trend and cycle indicators after a half-cycle dwell test
- 2000Constructing a dominant-cycle squelch trend filter
- 2000Phasor displays for dominant-cycle construction
- 2002Low-lag trendline from elliptic and dominant-cycle notches
- 2004Spectral peaks are mode diagnostics, not forecasts
- 2004Compressive last-stage oscillator construction
- 2013Constructing trend failure curves from qualified-trend transitions
- 2014Lookback range, a two-lag smoother, and next-bar fills
- 2014Constructing a MESA stochastic with roofing and SuperSmoother filters
- 2016Constructing spectral heatmaps for dominant market cycles