Survival probabilities of autoregressive processes
Abstract
Given an autoregressive process X of order p (i.e. Xn = a1 Xn-1 + ...+ ap Xnp + Yn where the random variables Y1, Y2, ... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending on the coefficients a1,...,ap and the distribution of Y1, we state conditions under which the survival probability decays polynomially, faster than polynomially or converges to a positive constant. Special emphasis is put on AR(2) processes.
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