2016issue C0916-17
Constructing spectral heatmaps for dominant market cycles
A market spectrum can be built as two readouts of the same power vector: one power-weighted dominant period and a period-by-period heatmap. That dual construction also keeps a short-sample maximum-entropy spectrum and a longer-sample Fourier baseline on their own lookbacks.
- A dominant-cycle estimate is a power-weighted average of candidate periods, and it is left unchanged when accumulated spectral power falls below 0.25.
- The same power vector can be drawn as a heatmap with one series for each integer period from 8 through 48, with color ramps switching at a spectral-power threshold of 0.5.
- Maximum-entropy spectra are described as usable on relatively short series, while Fourier analysis is described as most effective on series of six months or longer.
- Spectral dilation treats longer-period cycles as carrying proportionally larger amplitude swings.
Two outputs from one power vector
A market spectrum is treated here as a construction problem with two explicit outputs. The first output is a single power-weighted dominant period. The second is a period-by-period heatmap of the same power vector.
Spectral analysis is the broader practice of measuring how power is distributed across candidate cycle lengths so a dominant period can be identified and displayed. Both displays start from that power vector. The dominant-cycle line compresses it into one period. The heatmap keeps each integer length visible.
Forming the dominant-cycle estimate
A dominant-cycle estimate is formed as a power-weighted average of candidate periods whenever the accumulated power sum is not zero. If accumulated spectral power falls below 0.25, the construction keeps the previous dominant-cycle value instead of computing a new one.
That hold rule belongs to the construction. It is used when total spectral power is too weak to update the estimate.
Building the period heatmap
The heatmap construction plots a separate series for each integer period from 8 through 48. Heatmap color ramps switch at a spectral-power threshold of 0.5, while the third color channel is held at zero.
The two readouts do not replace each other. One number names the power-weighted period. The heatmap shows how that power is spread across the same candidate lengths.
Different lookbacks for each spectrum
Maximum-entropy spectrum analysis is presented as both a high-resolution cycle identifier and an adaptive-filtering method used with moving averages to project upper and lower trend channels. Maximum-entropy spectra are described as usable on relatively short series of prices, volume, open interest, or oscillator outputs.
Fourier analysis is described as most effective on series of six months or longer. A fast Fourier construction decomposes a series into sinusoids of different cycle lengths and converts the series from a time function into a frequency function.
Spectral dilation as a construction assumption
Spectral dilation is defined as the idea that market cycles with longer periods have proportionally larger amplitude swings. That idea is a construction assumption used when longer-period cycles are given proportionally larger amplitude swings. It is not a claim about a present market.
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