Given an autoregressive process X of order p(i.e.Xn = a1Xn−1 + ··· + apXn−p + Ynwhere the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the processdoes not exceed a constant barrier up to time N (survival or persistenceprobability). Depending on the coefficients a1,...,ap and the distribution ofY1, we state conditions under which the survival probabilitydecays polynomially, faster than polynomially or converges to a positive constant. Specialemphasis is put on AR(2) processes.
