Evaluating moving-average lag in cycle filters

Three averages on one series

A moving average is a lookback average of ordered price observations used as a baseline smoother or forecast of the local level. Exponential smoothing is a recursive smoother that weights recent observations more heavily than older ones over a defined sampling interval. A Hull moving average is a weighted moving-average construction designed to reduce lag relative to a simple average of the same lookback.

The archive workflow can place a 200-bar simple moving average, exponential moving average, and Hull moving average on the same price series as alternative smoothers of ordered observations. The three constructions then sit on one sample path so their lag and remaining roughness can be compared without changing the lookback.

The cycles a time frame can show

Chart time frame selects which cycles appear. A spectrogram of a daily, weekly, or hourly chart often shows about six visible cycles in a 10- to 140-bar wavelength range.

The trading cycle is the dominant cycle in the 10- to 50-bar band, the shorter swing a trader treats as the one to trade. The trend cycle is the dominant cycle in the 80- to 140-bar band, and its slope supplies trend context for that shorter swing.

Sampling noise is associated with periods below 10 bars, and cycle trading is treated as impractical for cycle lengths of 10 bars or less. A smoother that follows those short wavelengths is more likely to be tracking noise than a usable trading cycle.

Market mode from slope and amplitude

Market mode is whether price is better treated as trending or cycling. In this workflow it is evaluated as a relationship between trend-cycle slope and trading-cycle amplitude, not as a separate object from those two cycles.

A long lookback average can sit with the trend cycle while a faster construction sits closer to the trading cycle. Judging the smoother means asking which band it is actually following, then reading mode from slope versus amplitude rather than from a third label.

What hides the cycle

Four technical obstacles stand between the chart and cyclic structure: superimposed cycles, indicators not tuned to the relevant cycles, noise, and excessive indicator lag. If the average or the oscillator built from it is not tuned to the trading cycle or the trend cycle, the display can look orderly while the intended swing is already turning.

When divergence is an artifact

A momentum divergence on an unbounded oscillator tuned near the trading cycle can be an artifact of trend-cycle momentum rather than a timely reversal signal of the longer cycle. Editorial interpretation: name the band first, or trend-cycle slope can be misread as a completed turn in that longer cycle.