Moving Average (technical Analysis) - Weighted Moving Average

Weighted Moving Average

A weighted average is any average that has multiplying factors to give different weights to data at different positions in the sample window. Mathematically, the moving average is the convolution of the datum points with a fixed weighting function. One application is removing pixelisation from a digital graphical image.

In technical analysis of financial data, a weighted moving average (WMA) has the specific meaning of weights that decrease in arithmetical progression. In an n-day WMA the latest day has weight n, the second latest n − 1, etc., down to one.

The denominator is a triangle number equal to In the more general case the denominator will always be the sum of the individual weights.

When calculating the WMA across successive values, the difference between the numerators of WMA_M+1 and WMA_M is np_M+1 − p_M − ... − p_M−n+1. If we denote the sum p_M + ... + p_M−n+1 by Total_M, then

The graph at the right shows how the weights decrease, from highest weight for the most recent datum points, down to zero. It can be compared to the weights in the exponential moving average which follows.