Volume 18, 2014
|Page(s)||145 - 170|
|Published online||28 November 2013|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.