Extremes of Some Sub‐Sampled Time Series
Abstract
Let Xk be a stationary time series and y k=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 8) and offer more precise details for the class of linear models. Motivation comes from the comparison of schemes for monitoring financial and environmental processes.
Citing Literature
Number of times cited according to CrossRef: 4
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- Yu‐pin Hu, Identifying the time‐effect factors of multiple time series, Journal of Forecasting, 10.1002/for.948, 24, 5, (379-387), (2005).
