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Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models

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  • Zhang, Xiuzhen
  • Lu, Zhiping
  • Wang, Yangye
  • Zhang, Riquan

Abstract

In this paper, jackknife empirical likelihood is proposed to be applied in stationary time series models. By applying the jackknife method to Whittle estimator, we obtain new asymptotically independent pseudo samples which will be used to construct linear constraints for empirical likelihood. The jackknife empirical log-likelihood ratio is shown to follow a chi-square limiting distribution, which validates the corresponding confidence regions asymptotically. However, similar to the drawbacks of empirical likelihood, this method suffers from the non-definition problem and the inaccurate coverage probability in constructing confidence regions. So we further develop the adjusted jackknife empirical likelihood borrowing the idea of Chen et al. (2008) to improve the performance of the jackknife empirical likelihood. With a specific adjustment level, the adjusted jackknife empirical likelihood achieves a more high-order coverage precision than the classical jackknife empirical likelihood does and our simulations corroborate this point.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301334
    DOI: 10.1016/j.spl.2020.108830
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    References listed on IDEAS

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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. 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.
    3. Yang, Hanfang & Zhao, Yichuan, 2013. "Smoothed jackknife empirical likelihood inference for the difference of ROC curves," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 270-284.
    4. Zhong, Ping-Shou & Chen, Sixia, 2014. "Jackknife empirical likelihood inference with regression imputation and survey data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 193-205.
    5. 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.
    6. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    7. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    8. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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