×

Exit times for ARMA processes. (English) Zbl 1444.60022

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

MSC:

60F10 Large deviations
60G40 Stopping times; optimal stopping problems; gambling theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Software:

astsa
PDFBibTeX XMLCite
Full Text: DOI

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. · Zbl 1045.62081
[2] Baumgarten, C. (2014).Survival probabilities of autoregressive processes.ESAIM Prob. Statist.18,145-170. · Zbl 1339.60030
[3] Di Nardo, E. (2008).On the first passage time for autoregressive processes.Sci. Math. Jpn.67,137-152. · Zbl 1142.62060
[4] Högnäs, G. and Jung, B. (2010).Analysis of a stochastic difference equation: exit times and invariant distributions.Fasc. Math.44,69-74. · Zbl 1208.60072
[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.
[6] Jung, B. (2013).Exit times for multivariate autoregressive processes.Stoch. Process. Appl.123,3052-3063. · Zbl 1290.60029
[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.) · Zbl 1037.60500
[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. · Zbl 0723.60044
[9] Novikov, A. and Kordzakhia, N. (2008).Martingales and first passage times of AR(1) sequences.Stochastics80,197-210. · Zbl 1148.60061
[10] Ruths, B. (2008).Exit times for past-dependent systems.Survey Appl. Indust. Math.15,25-30. · Zbl 1199.60156
[11] Shumway, R. H. and Stoffer, D. S. (2011).Time Series Analysis and Its Applications,3rd edn.Springer,New York. · Zbl 1276.62054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.