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

2018/10/22 by Noonan, Jack, Zhigljavsky, Anatoly
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1810.09229

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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