Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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New Bootstrap Method for Autoregressive Models

  • Hwang, Eunju (Institute of Mathematical Sciences and Department of Statistics, Ewha Womans University) ;
  • Shin, Dong Wan (Institute of Mathematical Sciences and Department of Statistics, Ewha Womans University)
  • Received : 2012.10.10
  • Accepted : 2013.01.19
  • Published : 2013.01.31
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Abstract

A new bootstrap method combined with the stationary bootstrap of Politis and Romano (1994) and the classical residual-based bootstrap is applied to stationary autoregressive (AR) time series models. A stationary bootstrap procedure is implemented for the ordinary least squares estimator (OLSE), along with classical bootstrap residuals for estimated errors, and its large sample validity is proved. A finite sample study numerically compares the proposed bootstrap estimator with the estimator based on the classical residual-based bootstrapping. The study shows that the proposed bootstrapping is more effective in estimating the AR coefficients than the residual-based bootstrapping.

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References

  1. Bose, A. (1988). Edgeworth correction by bootstrap in autoregressions, Annals of Statistics, 16, 1709-1722. https://doi.org/10.1214/aos/1176351063
  2. Clements, M. P. and Kim, J. H. (2007). Bootstrap prediction intervals for autoregressive time series, Computational Statistics and Data Analysis, 51, 3580-3594. https://doi.org/10.1016/j.csda.2006.09.012
  3. Freedman, D. A. (1981). Bootstrapping regression models, Annals of Statistics, 9, 1218-1228. https://doi.org/10.1214/aos/1176345638
  4. Freedman, D. A. (1984). On bootstrapping two-stage least squares estimates in stationary linear models, Annals of Statistics, 12, 827-842. https://doi.org/10.1214/aos/1176346705
  5. Goncalves, S. and Kilian, L. (2004). Bootstrapping autoregressions with conditional heteroskedasticity of unknown form, Journal of Econometrics, 123, 89-120. https://doi.org/10.1016/j.jeconom.2003.10.030
  6. Goncalves, S. and Kilian, L. (2007). Asymptotic and bootstrap inference for AR(${\infty}$) processes with conditional heteroskedasticity, Econometric Reviews, 26, 609-641. https://doi.org/10.1080/07474930701624462
  7. Grigoletto, M. (1998). Bootstrap prediction intervals for autoregressions: Some alternatives, International Journal of Forecasting, 14, 447-456. https://doi.org/10.1016/S0169-2070(98)00004-1
  8. Hwang, E. and Shin, D.W. (2011). Stationary bootstrapping for non-parametric estimator of nonlinear autoregressive model, Journal of Time Series Analysis, 32, 292-303. https://doi.org/10.1111/j.1467-9892.2010.00699.x
  9. Hwang, E. and Shin, D. W. (2012a). Strong consistency of the stationary bootstrap under $\psi$-weak dependence, Statistics and Probability Letters, 82, 488-495. https://doi.org/10.1016/j.spl.2011.12.001
  10. Hwang, E. and Shin, D. W. (2012b). Stationary bootstrap for kernel density estimators under $\psi$-weak dependence, Computational Statistics and Data Analysis, 56, 1581-1593. https://doi.org/10.1016/j.csda.2011.10.001
  11. Kabaila, P. (1993). On bootstrap predictive inference for autoregressive processes, Journal of Time Series Analysis, 14, 473-484. https://doi.org/10.1111/j.1467-9892.1993.tb00158.x
  12. Kim, J. H. (2004). Bias-correcting bootstrap prediction regions for vector autoregression, Journal of Forecasting, 23, 141-154. https://doi.org/10.1002/for.908
  13. Lahiri, S. N. (1999). On second-order properties of the stationary bootstrap method for studentized statistics, In: Asymptotic, Nonparametrics, and Time Series, (Eds. Ghosh, S.), Marcel Dekker, New York, 683-711.
  14. Nordman, D. J. (2009). A note on the stationary bootstrap's variance, Annals of Statistics, 37, 359-370. https://doi.org/10.1214/07-AOS567
  15. Paparoditis, E. and Politis, D. N. (2005). Bootstrapping unit root tests for autoregressive time series, Journal of the American Statistical Association, 100, 545-553. https://doi.org/10.1198/016214504000001998
  16. Parker, C., Paparoditis, E. and Politis, D. N. (2006). Unit root testing via the stationary bootstrap, Journal of Econometrics, 133, 601-638. https://doi.org/10.1016/j.jeconom.2005.06.008
  17. Pascual, L., Romo, J. and Ruiz, E. (2004). Bootstrap predictive inference for ARIMA processes, Journal of Time Series Analysis, 25, 449-465. https://doi.org/10.1111/j.1467-9892.2004.01713.x
  18. Patton, A., Politis, D. N. and White, H. (2009). Correction to "Automatic block-length selection for the dependent bootstrap" by D. Politis and H. White, Econometric Reviews, 28, 372-375. https://doi.org/10.1080/07474930802459016
  19. Politis, D. N. (2003). The Impact of bootstrap methods on time series analysis, Statistical Science, 18, 219-230 https://doi.org/10.1214/ss/1063994977
  20. Politis, D. N. and Romano, J. P. (1994). The stationary bootstrap, Journal of the American Statistical Association, 89, 1303-1313. https://doi.org/10.1080/01621459.1994.10476870
  21. Politis, D. N. and White, H. (2004). Automatic block-length selection for the dependent bootstrap, Econometric Reviews, 23, 53-70. https://doi.org/10.1081/ETC-120028836
  22. Swensen, A. R. (2003). Bootstrapping unit root tests for integrated processes, Journal of Time Series Analysis, 24, 99-126. https://doi.org/10.1111/1467-9892.00295
  23. Thombs, L. A. and Schucany,W. R. (1990). Bootstrap prediction intervals for autoregression, Journal of the American Statistical Association, 95, 486-492.