Nonstationary and Seasonal Time Series Models

  • Peter J. Brockwell
  • Richard A. Davis
Part of the Springer Texts in Statistics book series (STS)


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.


Ordinary Little Square Unit Root ARMA Model ARIMA Model Generalize Little Square 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Peter J. Brockwell
    • 1
  • Richard A. Davis
    • 2
  1. 1.Royal Melbourne Institute of TechnologyMelbourneAustralia
  2. 2.Department of StatisticsColorado State UniversityFort CollinsUSA

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