Abstract.In this paper we consider the long‐run distribution of a multivariate autoregressive process of the formxn=An‐1xn‐1+ noise, where the noise has an unknown (possibly nonstationary and nonindependent) distribution andAnis a (generally) time‐varying transition matrix. It can easily be shown that the processxnneed not have a known long‐run distribution (in particular, central limit theorem effects do not generally hold). However, if the distribution of the noise approaches a known distribution asngets large, we show that the distribution ofxnmay also approach a known distribution for largen.Such a setting might occur, for example, when transient effects associated with the early stages of a system's operation die out. We first present a general result that applies for arbitrary noise distributions and generalAn. Several special cases are then presented that apply for noise distributions in the infinitely divisible class and/or for asymptotically constant coefficientAn. We illustrate the results on a problem in characterizing the asymptotic distribution of the estimation error in a Kalm
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