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Robust Inference For The Mean In The Presence Of Serial Correlation And Heavy-Tailed Distributions

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  • McElroy, Tucker
  • Politis, Dimitris N.

Abstract

The problem of statistical inference for the mean of a time series with possibly heavy tails is considered. We first show that the self-normalized sample mean has a well-defined asymptotic distribution. Subsampling theory is then used to develop asymptotically correct confidence intervals for the mean without knowledge (or explicit estimation) either of the dependence characteristics, or of the tail index. Using a symmetrization technique, we also construct a distribution estimator that combines robustness and accuracy: it is higher-order accurate in the regular case, while remaining consistent in the heavy tailed case. Some finite-sample simulations confirm the practicality of the proposed methods.

Suggested Citation

  • McElroy, Tucker & Politis, Dimitris N., 2002. "Robust Inference For The Mean In The Presence Of Serial Correlation And Heavy-Tailed Distributions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1019-1039, October.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:05:p:1019-1039_18
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    Cited by:

    1. Piotr Kokoszka & Michael Wolf, 2002. "Subsampling the mean of heavy-tailed dependent observations," Economics Working Papers 600, Department of Economics and Business, Universitat Pompeu Fabra.
    2. 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.
    3. Piotr Kokoszka & Michael Wolf, 2004. "Subsampling the mean of heavy‐tailed dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 217-234, March.

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