Model Selection Under Nonstationarity: Autoregressive Models and Stochastic Linear Regression Models

Abstract

We give sufficient conditions for strong consistency of estimators for the order of general nonstationary autoregressive models based on the minimization of an information criterion a la Akaike's (1969) AIC. The case of a time-dependent error variance is also covered by the analysis. Furthermore, the more general case of regressor selection in stochastic regression models is treated.