Empirical likelihood for stationary ARMA models based on inherent martingale structures

Yinghua Li and Yongsong Qin

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 20, 6476-6492

Abstract: Autoregressive moving average (ARMA) models with finite innovation variance are popular in practice and we utilize the inherent martingale structures of the models to construct empirical likelihood (EL) statistics and study the construction of EL confidence regions for the parameters in ARMA models with finite innovation variance, avoiding the choice of the block size in the blockwise EL (BEL) method. It is shown that the EL ratio statistics are asymptotically χ2-type distributed, which are used to obtain EL based confidence regions for the parameters in ARMA models with finite innovation variance. Simulation results show that the EL method proposed in this article is not only better than the normal approximation method, but also superior to the EL method in the frequency domain. In addition, simulation results also show that, for ARMA models with finite innovation variance, the EL method based on the self-weighted least absolute deviation (LAD) estimator does not show advantages over the EL method proposed in this article.

Date: 2025
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DOI: 10.1080/03610926.2025.2458185

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