The Estimation of the Order of an Autoregression Using Recursive Residuals and Cross‐validation

Several criteria for the estimation of the order of an autoregressive representation of a stationary time series are examined. There need not be a true finite‐order autoregression model for the data, so that the purpose of model identification is to obtain an adequate representation of the data. It is proved that minimizing the sum of squares of recursive residuals (the ‘predictive minimizing description length’) is equivalent to minimizing BIC. The equivalence between the cross‐validation and Akaike information criterion methods of autoregressive modelling is also established.