engleski

Extremal properties of multivariate moving average processes with random coefficients

We consider a class of multivariate moving average processes with stationary random matrix coefficients. If the noise sequence is regularly varying and independent of the sequence of random coefficients which are of lighter tail, the resulting stationary process is necessarily regularly varying. This result has been obtained in the case of iid coefficients by Resnick and Willekens (1991), but it holds more generally. It is known that the extremes of such process are in the maximum domain of attraction of Frechet distribution. However, we show that it is possible to analyze the extremal behavior of such processes in much greater detail. In particular, we present closed form expressions for the extremal index and the asymptotic cluster size probabilities for the norm of such processes.

Time series; moving average; regular variation; tail processes; extremal index

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