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Statistical inference for partially linear varying coefficient autoregressive models

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  • Feng Luo
  • Guoliang Fan

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.

Suggested Citation

  • Feng Luo & Guoliang Fan, 2025. "Statistical inference for partially linear varying coefficient autoregressive models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(21), pages 6761-6778, November.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:21:p:6761-6778
    DOI: 10.1080/03610926.2025.2461622
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