Moving Averages

More generally, weighted averages may also be used. Moving averages are also called running means or rolling averages. They are a special case of “filtering”, which is a general process that takes one time series and transforms it into another time series. The term “moving average” is used to describe this procedure because each average is computed by dropping the oldest observation and including the next observation. The averaging “moves” through the time series until zt is computed at each observation for which all elements of the average are available. Note that in the above examples, the number of data points in each average remains constant. Variations on moving averages allow the number of points in each average to change. For example, in a cumulative average, each value of the new series is equal to the sum of all previous values. Moving averages are used in two main ways: Two-sided (weighted) moving averages are used to “smooth” a time series in order to estimate or highlight the underlying trend; one-sided (weighted) moving averages are used as simple forecasting methods for time series. While moving averages are very simple methods, they are often building blocks for more complicated methods of time series smoothing, decomposition and forecasting.