On the localized estimators and generalized Akaike´s criterions

The problem of nonstationary system modelling is considered and the local modelling approach ts proposed for it´s solution. At the begining the concept of localized maximum likelihood estimators is introduced and applied to approximation of time-varying stochastic systems. Two types of such estimators, first based on the concept of weighting and the second based on the concept of data windowing are proposed and discussed in some detail In the case of autoregressire systems. The problem of the proper choice of the model structure is next considered. It is shown that the criterion for model order selection proposed by Akaike for the case of maximum likelihood estimation (Information Criterion) can be extended to the case of localized estimators.