Weighted Moving Average (WMA)

A weighted moving average (WMA) is a moving average in which the prices in the window are not treated equally: the most recent price counts most and the oldest counts least. In the usual linear form over $n$ periods, the newest price has a weight of $n$, the one before it $n - 1$, and so on down to 1. The result is a weighted average, $\text{WMA} = \sum w_i P_i / \sum w_i$, and the weights sum to $n(n + 1) / 2$. For three closing prices of 10, 11 and 13, oldest first, the WMA is $(1 \times 10 + 2 \times 11 + 3 \times 13) / 6 = 71 / 6 = 11.83$.

The simple moving average of the same prices is 11.33. The weighted version sits closer to the latest price and so turns sooner when the trend changes, at the cost of reacting more to noise. The exponential moving average serves the same purpose with weights that decline geometrically and never reach zero. All are lagging measures used among technical indicators.