Constructing moving averages: weights, smoothing and crossovers

A constructed series

A moving average is a constructed series that replaces raw observations with a rolling blend of current and prior values so direction is easier to inspect and a reversal can be judged against a benchmark.

Equal-weight windows

A simple moving average assigns each date the arithmetic mean of a fixed number of successive observations and then updates by including the newest observation while removing the oldest.

Periodicity is the chosen number of sampling intervals in a simple average. A longer setting lowers each observation's weight and increases smoothness.

In a three-period simple average each included observation has weight one-third, whereas in a nine-period simple average each has weight one-ninth, so a longer lookback reduces the influence of any single extreme observation.

Increasing the number of observations in a simple moving average produces a smoother series because each individual data point contributes less to the current value.

Exponential decay

An exponential moving average is specified by a smoothing constant rather than by a finite observation count, because every earlier observation remains in the value with successively smaller geometric weight.

The smoothing constant is the parameter that sets how much of each exponential update comes from the newest observation versus the previous exponential average.

Once a prior exponential average exists, the next value equals the smoothing constant times the newest observation plus one minus that constant times the previous exponential average.

An exponential average with a smoothing constant of one-third is more volatile than one with a smoothing constant of one-ninth, matching the rule that smaller per-observation weight yields a smoother path.

Support, resistance and reversal penetration

A moving average can serve as a constructed support or resistance reference, and a penetration through that line can be treated as confirmation that a reversal may have begun.

That one-line rule is a reversal penetration: a move through the average itself is treated as confirmation that direction may have changed.

Dual-horizon crossovers

A moving-average crossover is a two-line rule in which a shorter, more volatile average crossing a longer, smoother average is treated as a hypothesis that short-horizon and long-horizon direction have diverged.

A shorter, more volatile average crossing a longer, smoother average is constructed as a signal that the short-horizon direction has diverged from the long-horizon direction. An upside cross is the buy hypothesis and a downside cross is the sell hypothesis.

Smoother constructions, whether from longer periodicity or a smaller smoothing constant, produce fewer crossover signals and respond later than more volatile constructions.

What a historical pairing does not establish

Choosing periodicities or smoothing constants by which pairing looked best on past data describes that historical sample and does not establish that the same pairing will be best later.

The intended holding horizon and tolerance for false signals remain the design constraints.