Survival probabilities of autoregressive processes
Probability
2012-07-17 v1
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.
Cite
@article{arxiv.1207.3610,
title = {Survival probabilities of autoregressive processes},
author = {Christoph Baumgarten},
journal= {arXiv preprint arXiv:1207.3610},
year = {2012}
}