Markov chains, AR linear models, and regular variation

Abstract

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary distribution can be derived from that of the innovations, provided that the chain satisfies a certain monotonicity condition with respect to a gauge function. In the second part, we study random linear models with random coefficients defined by an explicit iterative scheme. We prove that the precise structure of the underlying chain affects the form of the associated spectral measure.