# Moving Average/Weighted

## Mathematical Definition: Weighted moving average

editIn technical analysis of financial data, a **weighted moving average** (WMA) has the specific meaning of weights that decrease in arithmetical progression.^{[1]} In an *n*-day WMA the latest day has weight *n*, the second latest *n* − 1, etc., down to one. These weights create a discrete probability distribution with:

- and

The weighted moving average can be calculated for with the discrete probability mass function at time , where is the initial day, when data collection of the financial data begins and the price/cost of a product at day . the price/cost of a product at day for an arbitrary day *x*.

The denominator is a triangle number equal to which creates a discrete probability distribution by:

The graph at the right shows how the weights decrease, from highest weight at day *t* for the most recent datum points, down to zero at day *t-n*.

In the more general case with weights the denominator will always be the sum of the individual weights, i.e.:

- and as weight for for the most recent datum points at day
*t*and as weight for the day , which is*n*-th day before the most recent day .

The discrete probability distribution is defined by:

The weighted moving average with arbitrary weights is calculated by:

This general approach can be compared to the weights in the exponential moving average in the following section.

- ↑ "Weighted Moving Averages: The Basics". Investopedia.