Survival probabilities of autoregressive processes
Technische Universität Braunschweig, Institut für Mathematische
Revised: 8 October 2012
Given an autoregressive process X of order p (i.e. Xn = a1Xn−1 + ··· + apXn−p + 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.
Mathematics Subject Classification: 60G15 / 60G50
Key words: Autoregressive process / autoregressive moving average / boundary crossing probability / one-sided exit problem / persistence probablity / survival probability
© EDP Sciences, SMAI, 2013