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Subsampling the mean of heavy‐tailed dependent observations

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  • Piotr Kokoszka
  • Michael Wolf

Abstract

. We establish the validity of subsampling confidence intervals for the mean of a dependent series with heavy‐tailed marginal distributions. Using point process theory, we focus on GARCH‐like time series models. We propose a data‐dependent method for the optimal block size selection and investigate its performance by means of a simulation study.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:2:p:217-234
    DOI: 10.1046/j.0143-9782.2003.00346.x
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    References listed on IDEAS

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    1. Piotr S. Kokoszka & Murad S. Taqqu, 1994. "Infinite Variance Stable Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 203-220, March.
    2. Cline, Daren B. H. & Brockwell, Peter J., 1985. "Linear prediction of ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 281-296, April.
    3. Piotr S. Kokoszka & Murad S. Taqqu, 2001. "Can One Use the Durbin–Levinson Algorithm to Generate Infinite Variance Fractional ARIMA Time Series?," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 317-337, May.
    4. 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.
    5. Berkes, István & Horváth, Lajos & Kokoszka, Piotr, 2003. "Estimation Of The Maximal Moment Exponent Of A Garch(1,1) Sequence," Econometric Theory, Cambridge University Press, vol. 19(4), pages 565-586, August.
    6. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
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    Cited by:

    1. Tianming Xu & Yuesong Wei, 2023. "Ratio Test for Mean Changes in Time Series with Heavy-Tailed AR( p ) Noise Based on Multiple Sampling Methods," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    2. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    3. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Bootstrap tests for structural change with infinite variance observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1985-1995, October.
    4. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Subsampling tests for the mean change point with heavy-tailed innovations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2157-2166.
    5. Chen, Zhanshou & Jin, Zi & Tian, Zheng & Qi, Peiyan, 2012. "Bootstrap testing multiple changes in persistence for a heavy-tailed sequence," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2303-2316.

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