What is a Moving Weighted Average?

John Lister

A moving weighted average is an average of multiple figures which has two specific characteristics. First, it gives added emphasis, or weight, to recent figures in preference to older figures. In addition, as a moving average, the set of figures used changes over time to remain up-to-date. The moving weighted average can be used for a wide variety of mathematical purposes, though one of the most common is for making forecasts for either a business or a market.

Using a moving average, on the 31st day of the year the average would cover days 2 to 31.
Using a moving average, on the 31st day of the year the average would cover days 2 to 31.

One example of a moving average would be if a store kept track of its average sales over the past thirty days. On the 30th day of the year, this average would cover days 1 to 30. On the 31st day of the year, the average would cover days 2 to 31. On the 32nd day of the year, the average would cover days 3 to 32, and so on.

The main advantage of this method is that it allows the store to get an idea of how sales have varied over time without the trend being heavily distorted by a single event. For example, if the store had spectacular sales one day thanks to a celebrity appearance, it would cause a spike on a traditional graph. With a moving average, these one-off effects would not be so visible and the graph would instead better show long-term trends such as seasonal variations.

A weighted average is one where the various numbers involved are not given equal weight. This is common in stock market indices where extra emphasis is given to the largest firms in the market. This avoids sudden movements in the stock of a minor company distorting the overall picture.

A moving weighted average brings together these two techniques. It applies its weighting based on how recent each figure is. The idea is to give greater emphasis to the most recent figures, while still taking some account of the past. In finance, it is usually used to get the benefits of the moving average while making sure not to miss strong signals from the most recent events.

Producing the moving weighted average is a simple mathematical process. As an example, to produce a five-day moving weighted average, you would multiply the current day's figure by five, the figure from yesterday by four, the figure from two days ago by three, the figure from three days ago by two, and the figure from four days ago by one. You would then add up the five resulting figures and divide the result by five to get the moving weighted average.

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