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

Jack Noonan; Anatoly Zhigljavsky

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arXiv · 1810.09229

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

Jack Noonan·Anatoly Zhigljavsky

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Abstract

In this paper 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.

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Jack Noonan, Anatoly Zhigljavsky. 2019-04-27. Approximations for the boundary crossing probabilities of moving sums of normal random variables. https://arxiv.org/abs/1810.09229

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