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Strong consistency of the stationary bootstrap under ψ-weak dependence

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  • Hwang, Eunju
  • Shin, Dong Wan

Abstract

This work deals with the stationary bootstrap of Politis and Romano (1994) for theψ-weakly dependent sequences proposed by Doukhan and Louhichi (1999), establishing strong consistency of the bootstrap sample variance and the bootstrap sample mean under the dependence structure for the observed process. This extends the results of Politis and Romano (1994) and Shao and Yu (1993).

Suggested Citation

  • Hwang, Eunju & Shin, Dong Wan, 2012. "Strong consistency of the stationary bootstrap under ψ-weak dependence," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 488-495.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:488-495
    DOI: 10.1016/j.spl.2011.12.001
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    References listed on IDEAS

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    1. Gonçalves, Sílvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1367-1384, December.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Goncalves, Silvia & de Jong, Robert, 2003. "Consistency of the stationary bootstrap under weak moment conditions," Economics Letters, Elsevier, vol. 81(2), pages 273-278, November.
    4. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    5. Eunju Hwang & Dong Wan Shin, 2011. "Stationary bootstrapping for non‐parametric estimator of nonlinear autoregressive model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 292-303, May.
    6. Paul Doukhan & Sana Louhichi, 2001. "Functional Estimation of a Density Under a New Weak Dependence Condition," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 325-341, June.
    7. Dehling, Herold & Wendler, Martin, 2010. "Central limit theorem and the bootstrap for U-statistics of strongly mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 126-137, January.
    8. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    9. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
    10. Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
    11. Coulon-Prieur, Clémentine & Doukhan, Paul, 2000. "A triangular central limit theorem under a new weak dependence condition," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 61-68, March.
    12. Shao, Qi-Man & Yu, Hao, 1993. "Bootstrapping the sample means for stationary mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 175-190, October.
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    Cited by:

    1. Hwang, Eunju & Shin, Dong Wan, 2015. "Stationary bootstrapping for semiparametric panel unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 14-25.
    2. Shin, Dong Wan & Hwang, Eunju, 2013. "Stationary bootstrapping for cointegrating regressions," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 474-480.
    3. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    4. Hwang, Eunju & Shin, Dong Wan, 2013. "Stationary bootstrapping realized volatility," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2045-2051.

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