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Stationary bootstrap for kernel density estimators under ψ-weak dependence

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  • Hwang, Eunju
  • Shin, Dong Wan

Abstract

Stationary bootstrap technique is applied for kernel-type estimators of densities and their derivatives of stationary ψ-weakly dependent processes. The ψ-weak dependence, introduced by Doukhan & Louhichi [Doukhan, P., Louhichi, S., 1999. A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications 84, 313–342], unifies weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The class of ψ-weakly dependent processes includes all weakly dependent processes of interest in statistics, containing such important processes as GARCH processes, threshold autoregressive processes, and bilinear processes. We obtain asymptotic validity for the stationary bootstrap in the density and derivatives estimation. A Monte-Carlo experiment compares the proposed method with other methods. Log returns of daily Dow Jones index are analyzed by the proposed method.

Suggested Citation

  • Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1581-1593
    DOI: 10.1016/j.csda.2011.10.001
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    1. Tran, Lanh Tat, 1992. "Kernel density estimation for linear processes," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 281-296, June.
    2. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
    3. 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.
    4. Yvonne H. S. Ho & Stephen M. S. Lee, 2008. "Iterated Bootstrap‐t Confidence Intervals for Density Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 295-308, June.
    5. Marc Hallin & Lanh T. Tran, 1996. "Kernel density estimation for linear processes: asymptotic normality and bandwidth selection," ULB Institutional Repository 2013/2055, ULB -- Universite Libre de Bruxelles.
    6. Kim, Tae Yoon & Cox, Dennis D., 1996. "Uniform strong consistency of kernel density estimators under dependence," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 179-185, February.
    7. Marc Hallin & Lanh Tran, 1996. "Kernel density estimation for linear processes: Asymptotic normality and optimal bandwidth derivation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 429-449, September.
    8. Chen, Jia, 2008. "Asymptotics of kernel density estimators on weakly associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3230-3237, December.
    9. 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.
    10. 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.
    11. Li, Fuchun & Tkacz, Greg, 2006. "A consistent bootstrap test for conditional density functions with time-series data," Journal of Econometrics, Elsevier, vol. 133(2), pages 863-886, August.
    12. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    13. 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.
    14. Schick, Anton & Wefelmeyer, Wolfgang, 2006. "Pointwise convergence rates and central limit theorems for kernel density estimators in linear processes," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1756-1760, October.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Tran, Lanh Tat, 1990. "Kernel density estimation under dependence," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 193-201, August.
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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. Barbeito, Inés & Cao, Ricardo, 2016. "Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 130-147.
    3. Yan Li & Liangjun Su & Yuewu Xu, 2015. "A Combined Approach to the Inference of Conditional Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-220, April.
    4. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    5. Hwang, Eunju & Shin, Dong Wan, 2013. "Stationary bootstrapping realized volatility," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2045-2051.
    6. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.

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