Geodesic
Survival probabilities of autoregressive processes
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 145-170

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/ps/2013031
Classification : 60G15, 60G50
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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/articles/10.1051/ps/2013031/
DO  - 10.1051/ps/2013031
LA  - en
ID  - PS_2014__18__145_0
ER  - 
%0 Journal Article
%A Baumgarten, Christoph
%T Survival probabilities of autoregressive processes
%J ESAIM: Probability and Statistics
%D 2014
%P 145-170
%V 18
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2013031/
%R 10.1051/ps/2013031
%G en
%F PS_2014__18__145_0
Baumgarten, Christoph. Survival probabilities of autoregressive processes. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 145-170. doi: 10.1051/ps/2013031

Cité par Sources :