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Extremes of Some Sub‐Sampled Time Series

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  • M. G. SCOTTO
  • K. F. TURKMAN
  • C. W. ANDERSON

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.

Suggested Citation

  • M. G. Scotto & K. F. Turkman & C. W. Anderson, 2003. "Extremes of Some Sub‐Sampled Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 579-590, September.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:5:p:579-590
    DOI: 10.1111/1467-9892.00320
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    References listed on IDEAS

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    1. M. E. Robinson & J. A. Tawn, 2000. "Extremal analysis of processes sampled at different frequencies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 117-135.
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    Cited by:

    1. Hall, A. & Scotto, M. G., 2003. "Extremes of sub-sampled integer-valued moving average models with heavy-tailed innovations," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 97-105, May.
    2. Scotto, M., 2005. "Extremes of a class of deterministic sub-sampled processes with applications to stochastic difference equations," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 417-434, March.

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