Survival probabilities of autoregressive processes. (28th November 2013) - Baumgarten, Christoph
Abstract : Given an autoregressive process X of order p ( i.e. X n  =  a 1 X n −1  + ··· +  a p X n − p  +  Y n where the random variables Y 1, Y 2, ... 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 a 1, ..., a p and the distribution of Y 1, 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.