Centered moving averages for trend construction

Start from a two-part price model

A usable construction starts from a two-part price model: random point-to-point movement plus cyclic movement of varying wavelength, magnitude, and phase. Point-to-point movement is the change between one sampled price and the next. Cyclic movement is the remaining component made of waves whose wavelength, magnitude, and phase all change.

A moving average is a running mean over a defined span of ordered observations. It reduces shorter cycles and leaves a smoother combination of longer-wavelength components.

Successive differences are not a next-bar forecast

In one 191-trading-day daily-difference sample there were 99 rises, 87 falls, and 4 unchanged prints, so directional probabilities sat near 50 percent and did not supply a next-bar forecast. The same sample showed 102 same-direction follow-throughs versus 87 reversals, and runs longer than about 10 successive same-direction moves almost never appeared. Once those successive-difference counts are inspected, point-to-point movement can be treated as essentially random.

Choose span against wavelength

A simple n-point average is a running total that adds the newest observation and drops the oldest. That construction reduces point-to-point movement plus cycles shorter than about twice the span. Span is the lookback length of the average and is related to a cycle wavelength by the ratio m. When m is an integer the cycle is removed from the average. When m is less than 1 the cycle is attenuated but its peaks and troughs stay in place.

A pair of moving averages can isolate a named cycle, such as a nominal 41-week wave, from weekly closes. Nominal wavelength is the average peak-to-peak or trough-to-trough length of that named cycle over a study window, not a fixed clock period. Wavelength then varies moderately while magnitude varies more, so turning times are bounded more tightly than amplitude.

Center the average before reading trend

Plotting the average without centering is a primary construction failure. A centered average is plotted with a lag of half its span so peaks and troughs align with the original series. A 200-day centered line lags 100 days. A nonlagged average is plotted at the latest bar and can reverse the apparent trend near turning points. In one 860-day window the uncentered line showed the wrong long-term direction for at least 25 percent of the time, especially around turns.

Bounded excursions and leftover ripple

Once the average is centered, price excursions around it stay bounded, which is the geometric basis for drawing channels. Residual short-span ripple can be reduced with a second or weighted average or with differences between averages and data.