Constructing moving averages and MACD from one price series

One ordered price series

A simple moving average, an exponential moving average, and MACD are each computed from ordered prices. The same series can carry all three constructions, so the lookback and the weighting stay visible.

Simple moving average

A simple moving average is constructed by summing the included prices and dividing by the number of observations. That construction is the arithmetic mean of the latest prices kept in the lookback.

Exponential moving average

An exponential moving average assigns greater weight to more recent prices and updates recursively from the prior exponential average. The smoothing multiplier applied to the newest price is defined as 2 divided by the lookback length plus one.

MACD from two exponential averages

MACD is constructed as the difference between two exponential moving averages. In the stated MACD construction, the fast line is a 12-period exponential average minus a 26-period exponential average, and the signal line is a nine-period exponential average of that difference.

Crossovers, floors, and momentum

A basic crossover construction compares a 50-day simple moving average with a 200-day simple moving average. A crossover is a change in rank between a shorter average and a longer average on the same series.

Rising MACD troughs are described as increasing momentum, and falling MACD peaks as fading momentum. Simple and exponential averages are described as dynamic floors or ceilings relative to price.

Lag from past prices

Because both averages and MACD are computed from past prices, their crossings can appear after a price move has already started. That delay is lag: the wait between a price turn and an average-based crossing, because both inputs are built from past observations.