1990issue C051-7
A channel signal-to-noise gate for dominant-cycle forecasts
A price series can be built as a noisy channel, with a short-term noise band inside a longer-term channel envelope. This article teaches a two-stage construction: estimate a dominant cycle with a spectral method, then withhold the associated trade until the envelope-to-noise-band ratio clears a stated decibel threshold.
- A price series can be built as a noisy channel: daily range and very short-term day-to-day variation form the noise band, and longer-term variation forms the channel envelope.
- Signal amplitude is the peak-to-peak span minus the noise-band width; the signal-to-noise ratio is that remainder divided by the noise-band width and may be written in decibels.
- The stated rule withholds a trade below 6 dB, a 4-to-1 ratio; a 6 dB cycle-content case remains usable, while zero cycle content scrambles the marks.
- The same gate is presented for cycle-based programs that measure cycle content, including constructions that apply maximum-entropy spectrum analysis to ordered price observations.
An editorial two-stage reading
This article is a TradersWeek construction note. The editorial aim is to teach two stages. First, estimate a dominant cycle with a spectral method on ordered price observations. Second, release that forecast only after the channel envelope’s ratio to the noise band clears a stated decibel threshold.
The archive itself states a withhold rule on trades and presents the same gate for cycle-based programs, including those that use maximum-entropy spectrum analysis. The two-stage release wording is editorial and is not an archive claim. The facts below stay with the noisy-channel model, the decibel marks, and that gate.
Price as a noisy channel
A price series can be built as a noisy channel. Daily range and very short-term day-to-day variation form the noise band. Longer-term variation forms the channel envelope.
One construction waits until the peak-to-peak variation of that envelope exceeds four times the width of the noise band.
Estimating the signal-to-noise ratio
Noise strength is taken as channel width near a high or low. Signal-plus-noise is the peak-to-peak span from an approximate lowest low to an approximate highest high. Signal amplitude is that span minus the channel width. The ratio of the remainder to the channel width is the signal-to-noise estimate.
Power ratios may be written in decibels, where 6 dB is a 4-to-1 ratio and 7 dB is a 5-to-1 ratio.
Slicing levels in the radar illustrations
In the radar-style illustrations, a 10 dB pulse is separated sharply enough that a slicing level can keep signal-plus-noise above the level and noise alone below it.
At 7 dB, labeled tangential sensitivity, a pulse can usually be identified. Typical errors are treating a noise spike as a pulse or missing a pulse that falls below the threshold. Identification worsens rapidly below 7 dB.
Cycle content
Cycle-based constructions call this ratio cycle content. A noise-free sine wave yields clean theoretical entries and stops. A 6 dB cycle-content case remains usable. A zero cycle-content case, where noise power equals cycle power, produces whippy reversals that scramble the marks.
Uniform-bounded noise has less fuzzy edges than Gaussian white noise, so tangential sensitivity can sit about 1 dB lower. A 6 dB sine wave plus that bounded noise is offered as a visual guide for a trading channel or cycle.
The six-decibel withhold rule
The stated thresholding rule withholds a trade when that ratio is below 6 dB. That 6 dB mark is a 4-to-1 ratio measured as peak-to-peak variation less noise-channel width, divided by noise-channel width.
The same gate is presented for cycle-based programs that measure cycle content, including constructions that apply maximum-entropy spectrum analysis to ordered price observations.
A generic noise experiment
A generic BASIC experiment superimposes uniform-probability noise on a pulse and a sine wave, then approximates Gaussian white noise by summing random events and scaling by the square root of the number of events.
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