Nonstationary and Seasonal Time Series Models

Abstract

In this chapter we shall examine the problem of finding an appropriate model for a given set of observations {x ₁ ,..., x _n } that are not necessarily generated by a stationary time series. If the data (a) exhibit no apparent deviations from stationarity and (b) have a rapidly decreasing autocovariance function, we attempt to fit an ARMA model to the mean-corrected data using the techniques developed in Chapter 5. Otherwise we look first for a transformation of the data that generates a new series with the properties (a) and (b). This can frequently be achieved by differencing, leading us to consider the class of ARIMA (autoregressive integrated moving average) models, defined in Section 6.1. We have in fact already encountered ARIMA processes. The model fitted in Example 5.1.1 to the Dow-Jones Utilities Index was obtained by fitting an AR model to the differenced data, thereby effectively fitting an ARIMA model to the original series. In Section 6.1 we shall give a more systematic account of such models.