Survival probabilities of autoregressive processes. (28th November 2013)

• Record Type: Journal Article
• Authors: Baumgarten, Christoph
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 145
• Page End: 170
• Publication Date: 2013-11-28
• Subjects: Autoregressive process, -- autoregressive moving average, -- boundary crossing probability, -- one-sided exit problem, -- persistence probablity, -- survival probability; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013031
• Languages: English
• ISSNs: 1292-8100

Abstract

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.