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.
Mots-clés : autoregressive process, autoregressive moving average, boundary crossing probability, one-sided exit problem, persistence probablity, survival probability
@article{PS_2014__18__145_0,
author = {Baumgarten, Christoph},
title = {Survival probabilities of autoregressive processes},
journal = {ESAIM: Probability and Statistics},
pages = {145--170},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013031},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2013031/}
}
TY - JOUR AU - Baumgarten, Christoph TI - Survival probabilities of autoregressive processes JO - ESAIM: Probability and Statistics PY - 2014 SP - 145 EP - 170 VL - 18 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2013031/ DO - 10.1051/ps/2013031 LA - en ID - PS_2014__18__145_0 ER -
Baumgarten, Christoph. Survival probabilities of autoregressive processes. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 145-170. doi : 10.1051/ps/2013031. http://www.numdam.org/articles/10.1051/ps/2013031/
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