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A Non-standard Empirical Likelihood for Time Series

Author

Listed:
  • 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.

Suggested Citation

  • Daniel J. Nordman & Helle Bunzel & Soumendra N. Lahiri, 2012. "A Non-standard Empirical Likelihood for Time Series," CREATES Research Papers 2012-55, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-55
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    File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_55.pdf
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    References listed on IDEAS

    as
    1. Zhang, Junjian, 2006. "Empirical likelihood for NA series," Statistics & Probability Letters, Elsevier, pages 153-160.
    2. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, pages 175-194.
    3. Francesco Bravo, 2009. "Blockwise generalized empirical likelihood inference for non-linear dynamic moment conditions models," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 208-231, July.
    4. Lin, Lu & Zhang, Runchu, 2001. "Blockwise empirical Euclidean likelihood for weakly dependent processes," Statistics & Probability Letters, Elsevier, pages 143-152.
    5. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
    6. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    7. 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, vol. 72(3), pages 343-366.
    8. Daniel J. Nordman, 2009. "Tapered empirical likelihood for time series data in time and frequency domains," Biometrika, Biometrika Trust, vol. 96(1), pages 119-132.
    9. Kiefer, Nicholas M., 2001. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel without Truncation," Working Papers 01-13, Cornell University, Center for Analytic Economics.
    10. Wu, Rongning & Cao, Jiguo, 2011. "Blockwise empirical likelihood for time series of counts," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 661-673, March.
    11. 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, vol. 96, pages 1088-1096, September.
    12. Politis, Dimitris N. & Romano, Joseph P., 1993. "On the sample variance of linear statistics derived from mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 155-167, March.
    13. Nicholas M. Kiefer & Timothy J. Vogelsang, 2002. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation," Econometrica, Econometric Society, vol. 70(5), pages 2093-2095, September.
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    Cited by:

    1. Zhang, Xianyang, 2016. "Fixed-smoothing asymptotics in the generalized empirical likelihood estimation framework," Journal of Econometrics, Elsevier, vol. 193(1), pages 123-146.
    2. Xianyang Zhang & Xiaofeng Shao, 2016. "On the coverage bound problem of empirical likelihood methods for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 395-421, March.

    More about this item

    Keywords

    Brownian motion; Confidence Regions; Stationarity; Weak Dependence;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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