Approximations for the boundary crossing probabilities of moving sums of normal random variables

Noonan, Jack and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2021. Approximations for the boundary crossing probabilities of moving sums of normal random variables. Communications in Statistics - Simulation and Computation 50 (11) , pp. 3547-3568. 10.1080/03610918.2019.1626889

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Abstract

In this article we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed theory for stationary Gaussian processes and to consider a number of approximations (some well known and some not). We bring particular attention to the strong performance of a newly developed approximation that corrects the use of continuous time results in a discrete time setting. Results of extensive numerical comparisons are reported. These results show that the developed approximation is very accurate even for small window length.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Taylor & Francis
ISSN:	0361-0918
Date of Acceptance:	24 May 2019
Last Modified:	04 Nov 2022 12:33
URI:	https://orca.cardiff.ac.uk/id/eprint/123532

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