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Adjusted Empirical Likelihood for Time Series Models

Author

Listed:
  • Ramadha D. Piyadi Gamage

    (Bowling Green State University)

  • Wei Ning

    (Bowling Green State University)

  • Arjun K. Gupta

    (Bowling Green State University)

Abstract

Empirical likelihood method has been applied to dependent observations by Monti (Biometrika, 84, 395–405 1997) through the Whittle’s estimation method. Similar asymptotic distribution of the empirical likelihood ratio statistic for stationary time series has been derived to construct the confidence regions for the parameters. However, Monti’s approach is valid only when the error terms follow a Gaussian distribution. Nordman and Lahiri (Ann. Statist., 34, 3019–50 2006) derived estimating functions and empirical likelihood ratio statistic using frequency domain empirical likelihood approach for non-Gaussian error term distributions. Nonetheless, the required numerical problem of computing profile empirical likelihood function which involves constrained maximization has no solution sometimes, which leads to the drawbacks of using the original version of the empirical likelihood ratio. In this paper, we propose an adjusted empirical likelihood ratio statistic to modify the one proposed by Nordman and Lahiri so that it guarantees the existence of the solution of the required maximization problem, while maintaining the similar asymptotic properties as Nordman and Lahiri obtained. Simulations have been conducted to illustrate the coverage probabilities obtained by the adjusted version for different time series models which are competitive to the ones based on Nordman and Lahiri’s version, especially for small sample sizes.

Suggested Citation

  • Ramadha D. Piyadi Gamage & Wei Ning & Arjun K. Gupta, 2017. "Adjusted Empirical Likelihood for Time Series Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 336-360, November.
    • Handle: RePEc:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0137-y
    DOI: 10.1007/s13571-017-0137-y
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    References listed on IDEAS

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    1. Chun Yip Yau, 2012. "Empirical likelihood in long‐memory time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 269-275, March.
    2. Liu, Yukun & Yu, Chi Wai, 2010. "Bartlett correctable two-sample adjusted empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1701-1711, August.
    3. Chan, Ngai Hang & Ling, Shiqing, 2006. "Empirical Likelihood For Garch Models," Econometric Theory, Cambridge University Press, vol. 22(3), pages 403-428, June.
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    Cited by:

    1. Feifan Jiang & Lihong Wang, 2018. "Adjusted blockwise empirical likelihood for long memory time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 319-332, June.
    2. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. Ramadha D. Piyadi Gamage & Wei Ning, 2020. "Inference for short‐memory time series models based on modified empirical likelihood," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 322-339, September.

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