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Bayesian empirical likelihood inference and order shrinkage for autoregressive models

Author

Listed:
  • Kai Yang

    (Changchun University of Technology)

  • Xue Ding

    (Changchun University of Technology)

  • Xiaohui Yuan

    (Changchun University of Technology)

Abstract

This paper considers the Bayesian empirical likelihood (BEL) inference and order shrinkage for a class of sparse autoregressive models without assuming the distributions for the errors. By introducing a nonparametric likelihood, parameters’ point and interval estimators, as well as some asymptotic properties of the estimators are obtained. By introducing a spike-and-slab prior, the order and the non-zero autoregressive coefficients of the model can be easily and accurately determined together via the Markov Chain Monte Carlo (MCMC) techniques. Simulation studies are conducted to evaluate the proposed methods. Finally, a real data example of the US industrial production index data set is applied to show the good performances of the BEL methods.

Suggested Citation

  • Kai Yang & Xue Ding & Xiaohui Yuan, 2022. "Bayesian empirical likelihood inference and order shrinkage for autoregressive models," Statistical Papers, Springer, vol. 63(1), pages 97-121, February.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:1:d:10.1007_s00362-021-01231-6
    DOI: 10.1007/s00362-021-01231-6
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    Cited by:

    1. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    2. Kai Yang & Luan Zhao & Qian Hu & Wenshan Wang, 2024. "Bayesian Quantile Regression Analysis for Bivariate Vector Autoregressive Models with an Application to Financial Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 64(4), pages 1939-1963, October.

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