On the localized estimators and generalized Akaike's criteria

The problem of nonstationary system modeling is considered and the local modeling approach is proposed for its solution. Initially, the concept of localized maximum likelihood estimators is introduced and applied to approximation of time-varying stochastic systems. Two types of such estimators, the 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 autoregressive systems, Next, the problem of the proper choice of the model structure is 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.