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 {x₁, …, x _n } that are not necessarily generated by a stationary time series. If the data (a) exhibit no apparent deviations from stationary 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.