Empirical likelihood inference for time-varying coefficient autoregressive models

Abstract

In this paper, we propose time-varying coefficient autoregressive models (TVARMs) of [Formula: see text]th order as a solution for capturing the nonlinear structure of multiple explanatory variables. The stationary [Formula: see text]-mixing sequence of autoregressive variables is considered. We apply empirical likelihood approach to investigate confidence regions of the autoregressive coefficients of the TVARMs, and establish the nonparametric version of Wilks’ theorem of the proposed empirical log-likelihood ratio. Further, the maximum empirical likelihood estimator of the autoregressive coefficients and its asymptotic distribution are also obtained. Besides, to determine the order of autoregression, penalized empirical likelihood approach is developed with the help of smoothly clipped absolute deviation penalty and the resultant penalized estimators have the oracle property. Simulation studies and an analysis of monthly Chinese price index dataset are used to demonstrate the effectiveness of our proposed methods.