Non-stationary Models

  • Paul S.P. Cowpertwait
  • Andrew V. Metcalfe
Part of the Use R book series (USE R)

As we have discovered in the previous chapters, many time series are nonstationary because of seasonal effects or trends. In particular, random walks, which characterise many types of series, are non-stationary but can be transformed to a stationary series by first-order differencing (§4.4). In this chapter we first extend the random walk model to include autoregressive and moving average terms. As the differenced series needs to be aggregated (or ‘integrated’) to recover the original series, the underlying stochastic process is called autoregressive integrated moving average, which is abbreviated to ARIMA.


White Noise GARCH Model ARIMA Model Residual Series Arch Model 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Inst. Information and Mathematical Sciences, Maasey UniversityAuckland, Albany CampusNew Zealand
  2. 2.School of Mathematical Sciences, University of AdelaideAustralia

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