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A unified approach to self-normalized block sampling

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  • Bai, Shuyang
  • Taqqu, Murad S.
  • Zhang, Ting

Abstract

The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range dependent, or whether it has a light or heavy-tailed marginal distribution. In the current paper, we develop an asymptotic theory for the self-normalized block sampling, and prove that the corresponding block sampling method can provide a unified inference approach for the aforementioned different situations in the sense that it does not require the a priori estimation of auxiliary parameters. Monte Carlo simulations are presented to illustrate its finite-sample performance. The R function implementing the method is available from the authors.

Suggested Citation

  • Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:8:p:2465-2493
    DOI: 10.1016/j.spa.2016.02.007
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