Constructing minimum tradable cycles from spectral noise

Why a noise measure comes first

A simple moving average is presented as a basic reading of a price series. Values above the average are treated as an advance and values below as a decline.

Before cycles are hunted in a price series, a noise measure is required, because a simple moving average is said to need cyclic variation in order to operate.

How cycle energy is located

Fourier-family transforms and maximum-entropy spectral analysis are listed as ways to locate cycle energy. A discrete or fast Fourier transform produces a spectral plot whose peaks mark where sine-cosine energy concentrates.

Representative spectra are described as increasing in magnitude toward longer wavelengths, with many short cycles treated as small-magnitude noise.

Turning bar-range uncertainty into a floor

Average-range noise is a smoothed high-minus-low range used as a bar-level estimate of unobserved intra-period path uncertainty. One illustrated daily series used a 75-bar lookback.

The path inside a bar is treated as unobserved, so a crossover fill is assumed to occur somewhere inside the high-low range rather than at a known price.

A theoretical lower signal-to-noise ratio of one half is derived by assuming worst-case fills at the noise extremes around a unit-magnitude sine wave whose peak-to-peak span is 2. A practical construction floor near 2 is then proposed as about four times that theoretical minimum.

The first peak above the cycle cutoff

The minimum tradable cycle is the first spectral peak above a cycle cutoff equal to the chosen signal-to-noise ratio times the measured noise level. With noise 0.381 and a ratio of 2 the cutoff is 0.762, and the illustrated first peak is 207.7 trading days at magnitude 1.032.

Shorter peaks are treated as below the noise floor. The cutoff is described as a low-pass rule that can admit longer peaks but not shorter ones.

Sizing the moving-average crossover after the cutoff

After a tradable wavelength is selected, a moving-average crossover period is often set to half that wavelength or slightly less.

TradersWeek editorial note: apply that half-wavelength habit only after the cutoff gate has already dropped shorter peaks. The archive states the length choice and the low-pass rule. It does not describe the sequence as a two-gate design.