Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables

Jack Noonan () and Anatoly Zhigljavsky ()
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Jack Noonan: Cardiff University
Anatoly Zhigljavsky: Cardiff University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 3, 873-892

Abstract: Abstract In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary Gaussian processes. By then subsequently correcting approximations for discrete time, we show that the developed approximations are very accurate even for a small window length. Also, they have high accuracy when the original r.v. are not exactly normal and when the weights in the moving window are not all equal. We then provide accurate and simple approximations for ARL, the average run length until crossing the boundary.

Keywords: Moving sum; Boundary crossing probability; Moving sum of normal; Change-point detection; Primary: 60G50; 60G35; Secondary: 60G70; 94C12; 93E20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-019-09769-7

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