# Survival probabilities of autoregressive processes

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 145-170
- ISSN: 1292-8100

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topBaumgarten, Christoph. "Survival probabilities of autoregressive processes." ESAIM: Probability and Statistics 18 (2014): 145-170. <http://eudml.org/doc/274344>.

@article{Baumgarten2014,

abstract = {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.},

author = {Baumgarten, Christoph},

journal = {ESAIM: Probability and Statistics},

keywords = {autoregressive process; autoregressive moving average; boundary crossing probability; one-sided exit problem; persistence probablity; survival probability; autoregressive processes; asymptotic behaviour},

language = {eng},

pages = {145-170},

publisher = {EDP-Sciences},

title = {Survival probabilities of autoregressive processes},

url = {http://eudml.org/doc/274344},

volume = {18},

year = {2014},

}

TY - JOUR

AU - Baumgarten, Christoph

TI - Survival probabilities of autoregressive processes

JO - ESAIM: Probability and Statistics

PY - 2014

PB - EDP-Sciences

VL - 18

SP - 145

EP - 170

AB - 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.

LA - eng

KW - autoregressive process; autoregressive moving average; boundary crossing probability; one-sided exit problem; persistence probablity; survival probability; autoregressive processes; asymptotic behaviour

UR - http://eudml.org/doc/274344

ER -

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