A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5.

Wang, Zheqi; Wang, Dehui; Cheng, Jianhua

This paper uses the empirical likelihood (EL) method for a new random coefficient autoregressive process driven by explanatory variables and past observations through logistic structure (OD-RCAR (1)), which combines explanatory variables and past observations, and puts forward the penalized maximum empirical likelihood (PMEL) method for parameters estimation and variable selection. Firstly, limiting distributions of the estimating function and log empirical likelihood ratio statistics based on EL are established. Meanwhile, this paper sets up a confidence region and EL test for parameters. Secondly, the maximum empirical likelihood estimators and their asymptotic properties are obtained. At the same time, the penalized empirical likelihood ratio test statistic is given. Thirdly, it is proved in a high-dimensional setting that the PMEL in our model can solve the problem of order selection and parameter estimation. Finally, not only practical data applications but also numerical simulations are adopted in order to describe the performance of proposed methods.

AUTOREGRESSIVE models; CONFIDENCE regions (Mathematics); LIKELIHOOD ratio tests; MAXIMUM likelihood statistics; PARAMETER estimation

Statistical Methods & Applications, 2023, Vol 32, Issue 2, p619

1618-2510

Academic Journal

10.1007/s10260-022-00671-0