The distribution of nonstationary autoregressive processes under general noise conditions

This paper considers the large-sample distribution of a multivariate autoregressive process of the form x/sub n/=A/sub n-1/x/sub n-1/+noise, where the noise has an unknown distribution and A/sub n/ is a (generally) time-varying transition matrix. It can be easily shown that the process x/sub n/ need not have a known large-sample distribution (in particular, central limit theorem effects do not generally hold). However, if the distribution of the noise approaches a known distribution as n gets large, we show that the distribution of x/sub n/ may also approach a known distribution for large n. Such results have applications in, e.g., adaptive tracking, filtering, model validation, etc.<<ETX>>