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Extremes of Some Sub‐Sampled Time Series
Author(s) -
SCOTTO M. G.,
TURKMAN K. F.,
ANDERSON C. W.
Publication year - 2003
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00320
Subject(s) - mathematics , series (stratigraphy) , limiting , sampling (signal processing) , point process , convergence (economics) , maxima , class (philosophy) , process (computing) , interval (graph theory) , discrete mathematics , statistics , combinatorics , computer science , mechanical engineering , art , paleontology , artificial intelligence , performance art , engineering , economics , computer vision , biology , art history , economic growth , operating system , filter (signal processing)
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.