Now that we have explored methods to estimate the parameters of an appropriately chosen model we turn to one of the main purposes of time series analysis, forecasting or predicting the future values of a series. In this section we discuss some forecasting methods commonly used in time series analysis. We first present the best linear predictor and its derivation in the infinite sample limit. Then we derive the approximate best linear predictor often used to speed up the calculation. We show how to write a program to update the prediction formula when new data are available and also introduce the simple exponential smoothing forecast procedure.