RATE OF POISSON APPROXIMATION OF THE NUMBER OF EXCEEDANCES OF NONSTATIONARY NORMAL SEQUENCES

It is known that the partial maximum of nonstationary Gaussian sequenc es converges in distribution and that the number of exceedances of a b oundary is asymptotically a Poisson random variable, under certain res trictions. We investigate the rate of Poisson approximation for the nu mber of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound c annot be improved.