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Bootstrap with larger resample size for root-n consistent density estimation with time series data

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  • Chang, Christopher C.
  • Politis, Dimitris N.

Abstract

We consider finite-order moving average and nonlinear autoregressive processes with no parametric assumption on the error distribution, and present a kernel density estimator of a bootstrap series that estimates their marginal densities root-n consistently. This is equal to the rate of the best known convolution estimators, and is faster than the standard kernel density estimator. We also conduct simulations to check the finite sample properties of our estimator, and the results are generally better than corresponding results for the standard kernel density estimator.

Suggested Citation

  • Chang, Christopher C. & Politis, Dimitris N., 2011. "Bootstrap with larger resample size for root-n consistent density estimation with time series data," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 652-661, June.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:6:p:652-661
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    References listed on IDEAS

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    1. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 73-87, December.
    2. Politis, Dimitris N. & Romano, Joseph P. & Wolf, Michael, 1999. "On the asymptotic theory of subsampling," DES - Working Papers. Statistics and Econometrics. WS 6334, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. J. Franke & J.‐P. Kreiss & E. Mammen & M. H. Neumann, 2002. "Properties of the nonparametric autoregressive bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(5), pages 555-585, September.
    4. Saavedra, Ángeles & Cao, Ricardo, 1999. "Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 129-155, April.
    5. Datta, Somnath, 1995. "On a modified bootstrap for certain asymptotically nonnormal statistics," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 91-98, August.
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    Cited by:

    1. Delaigle, Aurore & Meister, Alexander & Rombouts, Jeroen, 2016. "Root-T consistent density estimation in GARCH models," Journal of Econometrics, Elsevier, vol. 192(1), pages 55-63.

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