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Exit times for ARMA processes

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 February 2019

Timo Koski ,
Brita Jung  and
Göran Högnäs
Timo Koski*
Affiliation:
KTH Royal Institute of Technology
Brita Jung*
Affiliation:
Åbo Akademi University
Göran Högnäs*
Affiliation:
Åbo Akademi University
*
Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden. Email address: [email protected]
Department of Natural Sciences, Åbo Akademi University, FIN-20500 Åbo, Finland. Email address: [email protected]
Department of Natural Sciences, Åbo Akademi University, FIN-20500 Åbo, Finland. Email address: [email protected]
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Abstract

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We study the asymptotic behaviour of the expected exit time from an interval for the ARMA process, when the noise level approaches 0.

Keywords

ARMA modelautoregressiveexit timefirst passage timestationary distribution

MSC classification

Primary: 60G17: Sample path properties
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 191 - 195
Copyright
Copyright © Applied Probability Trust 2018 

References

[1]Basak, G. K. and Ho, K-W. R. (2004).Level-crossing probabilities and first-passage times for linear processes.Adv. Appl. Prob. 36,643–666.Google Scholar
[2]Baumgarten, C. (2014).Survival probabilities of autoregressive processes.ESAIM Prob. Statist. 18,145–170.Google Scholar
[3]Di Nardo, E. (2008).On the first passage time for autoregressive processes.Sci. Math. Jpn. 67,137–152.Google Scholar
[4]Högnäs, G. and Jung, B. (2010).Analysis of a stochastic difference equation: exit times and invariant distributions.Fasc. Math. 44,69–74.Google Scholar
[5]Jaskowski, M. and van Dijk, D. (2016). First-passage-time in discrete time and intra-horizon risk measures. Preprint. Available at https://sites.google.com/site/marcinjaskowski1/home/research.Google Scholar
[6]Jung, B. (2013).Exit times for multivariate autoregressive processes.Stoch. Process. Appl. 123,3052–3063.Google Scholar
[7]Klebaner, F. K. and Liptser, R. S. (1996).Large deviations for past-dependent recursions.Prob. Inf. Trans. 32,320–330. (Revised 2006 preprint: available at https://arxiv.org/abs/math/0603407v1.)Google Scholar
[8]Novikov, A. A. (1990).On the first passage time of an autoregressive process over a level and an application to a `disorder' problem.Theory Prob. Appl. 35,269–279.Google Scholar
[9]Novikov, A. and Kordzakhia, N. (2008).Martingales and first passage times of AR(1) sequences.Stochastics 80,197–210.Google Scholar
[10]Ruths, B. (2008).Exit times for past-dependent systems.Survey Appl. Indust. Math. 15,25–30.Google Scholar
[11]Shumway, R. H. and Stoffer, D. S. (2011).Time Series Analysis and Its Applications,3rd edn.Springer,New York.Google Scholar