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Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance

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  • Jinyu Li
  • Wei Liang
  • Shuyuan He

Abstract

This paper proposes a profile empirical likelihood for the partial parameters in ARMA(p, q) models with infinite variance. We introduce a smoothed empirical log‐likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method.

Suggested Citation

  • Jinyu Li & Wei Liang & Shuyuan He, 2014. "Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:868970
    DOI: 10.1155/2014/868970
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    References listed on IDEAS

    as
    1. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted least absolute deviations estimation for ARMA models with infinite variance," LSE Research Online Documents on Economics 5405, London School of Economics and Political Science, LSE Library.
    2. Li, Jinyu & Liang, Wei & He, Shuyuan, 2011. "Empirical likelihood for LAD estimators in infinite variance ARMA models," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 212-219, February.
    3. Li, Jinyu & Liang, Wei & He, Shuyuan & Wu, Xianbin, 2010. "Empirical likelihood for the smoothed LAD estimator in infinite variance autoregressive models," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1420-1430, September.
    4. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted Least Absolute Deviations Estimation For Arma Models With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 23(5), pages 852-879, October.
    5. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
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