For stationary or nearly stationary data, the exponential moving average is a simple method for time-series forecasting. Choose between forecasting and smoothing to see the difference between them; is the smoothing parameter in the exponential moving average and is the mean square error between the forecast (red curve) and actual values of the data (blue curve). Larger values of cause less smoothing.

The forecast at time is given by where is the actual value of the time series at time . This recursion starts at . When , the forecast is for all time and when , the forecast is the last observation. For more information on forecasting with exponential smoothing methods, see [1].

Students should ask themselves: is there any relationship between the appearance of the data and the optimum value of for forecasting? Why isn't the exponential moving average a very good forecasting method for data with a trend?

Reference

[1] S. G. Makridakis, S. C. Wheelwright, and R. J. Hyndman, Forecasting, Methods and Applications, 3rd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1998.