Abstract
In this chapter we shall examine the problem of selecting an appropriate model for a given set of observations n{X t , t = 1,…, n} data (a) exhibits no apparent deviations from stationarity and (b) has a rapidly decreasing autocorrelation function, we shall seek a suitable ARMA process to represent the mean-corrected data. If not, then we shall first look for a transformation of the data which 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) processes which is introduced in Section 9.1. Once the data has been suitably transformed, the problem becomes one of finding a satisfactory ARMA(p, q) model, and in particular of choosing (or identifying) p and q. The sample autocorrelation and partial autocorrelation functions and the preliminary estimators \({\hat \phi _m}\) and \({\hat \theta _m}\) of Sections 8.2 and 8.3 can provide useful guidance in this choice. However our prime criterion for model selection will be the AICC, a modified version of Akaike’s AIC, which is discussed in Section 9.3. According to this criterion we compute maximum likelihood estimators of φ, θ and σ2 for a variety of competing p and q values and choose the fitted model with smallest AICC value. Other techniques, in particular those which use the R and S arrays of Gray et al. (1978), are discussed in the recent survey of model identification by de Gooijer et al. (1985).
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© 1991 Springer Science+Business Media New York
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Brockwell, P.J., Davis, R.A. (1991). Model Building and Forecasting with ARIMA Processes. In: Time Series: Theory and Methods. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0320-4_9
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DOI: https://doi.org/10.1007/978-1-4419-0320-4_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-0319-8
Online ISBN: 978-1-4419-0320-4
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