The order determination 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. When a family of models includes (or is assumed to include) the true system, the consistency of the estimated model has, for example, been studied recently by using the maximum entropy criterion as a measure of fit. However, to establish this test, stationarity and the knowledge of the p. d. f. for the observed data are required. In this paper we define a criterion of measure of fit which enables us to treat the non-stationary case without knowledge of the p.d.f. of the data or without specifying the p. d. f. of model outputs. Based on this criterion, we study the order determination problem for the linear time-varying AR models.