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.

本文考虑了一类稀疏自回归模型的贝叶斯经验似然（BEL）推断和阶数收缩，而没有假设误差的分布。通过引入非参数似然，可以获得参数的点和区间估计量，以及估计量的一些渐近性质。通过引入先验后验的模型，可以通过马尔可夫链蒙特卡洛（MCMC）技术轻松，准确地确定模型的阶数和非零自回归系数。进行仿真研究以评估所提出的方法。最后，以美国工业生产指数数据集的真实数据示例为例，展示了BEL方法的良好性能。