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A Non-standard Empirical Likelihood for Time Series

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  • Daniel J. Nordman

    ()
    (Department of Statistics, Iowa State University)

  • Helle Bunzel

    ()
    (Department of Economics, Iowa State University & CREATES)

  • Soumendra N. Lahiri

    ()
    (Department of Statistics, Texas A&M University)

Abstract

Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though non-standard, data-blocking rule which uses a data block of every possible length. Consequently, the method involves no block selection and is also anticipated to exhibit better coverage performance. Its non-standard blocking scheme, however, induces non-standard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi-square one, but is distribution-free and can be reproduced through straightforward simulations. Numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard BEL.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-55.

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Length: 27
Date of creation: 03 Dec 2012
Date of revision:
Handle: RePEc:aah:create:2012-55

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Web page: http://www.econ.au.dk/afn/

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Keywords: Brownian motion; Confidence Regions; Stationarity; Weak Dependence;

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  1. Xiaofeng Shao, 2010. "A self-normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 72(3), pages 343-366.
  2. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2006. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1545, Cowles Foundation for Research in Economics, Yale University.
  3. Francesco Bravo, 2009. "Blockwise generalized empirical likelihood inference for non-linear dynamic moment conditions models," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 12(2), pages 208-231, 07.
  4. Politis, Dimitris N. & Romano, Joseph P., 1993. "On the sample variance of linear statistics derived from mixing sequences," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 45(1), pages 155-167, March.
  5. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 695-714, May.
  6. Lin, Lu & Zhang, Runchu, 2001. "Blockwise empirical Euclidean likelihood for weakly dependent processes," Statistics & Probability Letters, Elsevier, Elsevier, vol. 53(2), pages 143-152, June.
  7. Wu, Rongning & Cao, Jiguo, 2011. "Blockwise empirical likelihood for time series of counts," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(3), pages 661-673, March.
  8. Bunzel H. & Kiefer N. M. & Vogelsang T. J., 2001. "Simple Robust Testing of Hypotheses in Nonlinear Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1088-1096, September.
  9. Kiefer, Nicholas M., 2001. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel without Truncation," Working Papers, Cornell University, Center for Analytic Economics 01-13, Cornell University, Center for Analytic Economics.
  10. Daniel J. Nordman, 2009. "Tapered empirical likelihood for time series data in time and frequency domains," Biometrika, Biometrika Trust, Biometrika Trust, vol. 96(1), pages 119-132.
  11. Francesco Bravo, 2005. "Blockwise empirical entropy tests for time series regressions," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 26(2), pages 185-210, 03.
  12. Zhang, Junjian, 2006. "Empirical likelihood for NA series," Statistics & Probability Letters, Elsevier, Elsevier, vol. 76(2), pages 153-160, January.
  13. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
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