Statistical inference for partially linear varying coefficient autoregressive models

Feng Luo and Guoliang Fan

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 21, 6761-6778

Abstract: This article introduces partially linear varying coefficient autoregressive models to accommodate the nonlinear structure. We apply the profile least squares and B-spline approximation methods to estimate both the regression parameters and the nonlinear coefficient functions. To address potential spurious covariates in the linear component, we propose a penalized least squares approach aided by basis function approximations and smoothly clipped absolute deviation penalty. The consistency of this procedure and the oracle property of the regularized estimators are rigorously demonstrated. Furthermore, we perform a profile likelihood ratio test to check a linear hypothesis regarding the parameters of interest. Simulation studies and real data analysis are conducted to illustrate the finite sample performance of the proposed approaches.

Date: 2025
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DOI: 10.1080/03610926.2025.2461622

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