Extremes of Some Sub‐Sampled Time Series

M. G. Scotto, K. F. Turkman and C. W. Anderson

Journal of Time Series Analysis, 2003, vol. 24, issue 5, 579-590

Abstract: Let Xk be a stationary time series and yk=XkM be the sub‐sampled series corresponding to a fixed systematic sampling interval M > 1. In this paper, we use a point process approach to study the effect of the sub sampling on the extremal properties of Yk when Xk is a linear process with heavy‐tailed innovations. We prove complete point process convergence theorems which enable us to give in detail the weak limiting behaviour of maxima of the sub‐sampled process and to compare it with that of the original process. The results both exemplify the findings of a study by Robinson and Tawn (2000) and offer more precise details for the class of linear models. Motivation comes from the comparison of schemes for monitoring financial and environmental processes.

Date: 2003
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