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.

Keywords: 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://archive.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://archive.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, Volume 18 (2014), pp. 145-170. doi : 10.1051/ps/2013031. http://archive.numdam.org/articles/10.1051/ps/2013031/

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