ABSTRACT
This chapter discusses the problem of fitting a suitable model to an observed time series. One way that estimating a time-series mean differs from the rest of Statistics is that any results depend upon the underlying process having a property called ergodicity. The correlogram is helpful in trying to identify a suitable class of models for a given time series, and, in particular, for selecting the most appropriate type of autoregressive integrated moving average (ARIMA) model. In Box-Jenkins ARIMA modelling, the general approach is to difference an observed time series until it appears to come from a stationary process. The estimation problems for an autoregressive moving average model are similar to those for a moving average model in that an iterative procedure has to be used. When a model has been fitted to a time series, it is advisable to check that the model really does provide an adequate description of the data.
