Survival probabilities of autoregressive processes

Christoph Baumgarten

ESAIM: Probability and Statistics (2014)

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

Abstract

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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.

How to cite

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Baumgarten, 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 -

References

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