Approximations of the boundary crossing probabilities for the maximum of moving sums
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In this paper we study approximations for boundary crossing probabilities for the maximum of 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. Also, it has high precision when the original r.v. are not exactly normal and when the weights in the moving window are not equal.
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