Extremes of Some Sub-Sampled Time Series

Authors: SCOTTO M.G.; TURKMAN K.F.; ANDERSON C.W.

Source: Journal of Time Series Analysis, Volume 24, Number 5, September 2003 , pp. 579-590(12)

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Abstract:

Let X_k be a stationary time series and y_k=X_kM 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 Y_k when X_k 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.

Keywords: Linear Processes; extreme values; extremal index; point processes

Document Type: Research article

DOI: http://dx.doi.org/10.1111/1467-9892.t01-1-00320

Affiliations: 1: University of Aveiro, University of Lisbon, University of Sheffield

Publication date: 2003-09-01