Review Articles

Empirical likelihood inference in autoregressive models with time-varying variances

Yu Han ,

Chunming Zhang

Pages 129-138 | Received 25 Dec. 2020, Accepted 05 Apr. 2021, Published online: 22 Apr. 2021,
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This paper develops the empirical likelihood (EL) inference procedure for parameters in autoregressive models with the error variances scaled by an unknown nonparametric time-varying function. Compared with existing methods based on non-parametric and semi-parametric estimation, the proposed test statistic avoids estimating the variance function, while maintaining the asymptotic chi-square distribution under the null. Simulation studies demonstrate that the proposed EL procedure (a) is more stable, i.e., depending less on the change points in the error variances, and (b) gets closer to the desired confidence level, than the traditional test statistic.


  • Xu, K. L., & Phillips, P. C. B. (2008). Adaptive estimation of autroregressive models with time-varying variances. Journal of Econometrics, 142, 265280.
  • Variyath, A. M., & Chen, J. H. (2010). Abraham B. Empirical likelihood based variable selection. Journal of Statistical Planning and Inference, 140, 971981.
  • Watson, G. S. (1964). Smooth regression analysis. Sankhya Series A, 26, 359372.
  • Wong, W. H. (1983). On the consistency of cross validation in kernel nonparametric regression. Annals of Statistics, 11, 11361141.
  • Zhou, M., & Li, G. (2008). Empirical likelihood analysis of the Buckley-James estimator. Journal of Multivariate Analysis, 99, 649664.

To cite this article: Yu Han & Chunming Zhang (2021): Empirical likelihood inference in
autoregressive models with time-varying variances, Statistical Theory and Related Fields, DOI:
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