Dynamics of Model Overfitting Measured in terms of Autoregressive Roots

One method of describing the properties of a fitted autoregressive model of order p is to show the p roots that are implied by the lag operator. Considering autoregressive models fitted to 215 US macro series, with lags chosen by either the Bayesian or Schwarz information criteria or Akaike information criteria, the roots are found to constitute a distinctive pattern. Later analysis suggests that much of this pattern occurs because of overfitting of the models. An extension of the results shows that they have some practical multivariate time-series modelling implications. Copyright 2006 Blackwell Publishing Ltd.