The order determination problem for linear time-varying AR models

We are often faced with the problem of estimating the number of parameters, as well as their values, for a model that will fit a given set of observations. An important study of this identification problem was made by Akaike, who improved the maximum likelihood principle and established the so-called AIC criterion to select suitable models. This criterion has been applied extensively to constant coefficient AR models. The question of validity of the AIC approach for more general models appears to be open. Motivated by the desire to model nonstationary geophysical data the main purpose of this paper is to establish conditions guaranteeing the validity of the AIC approach to a class of time-varying AR models.