For complicated time series data, we study a kind of partially varying-coefficient autoregressive mixed model including the delay term of the dependent variable as part of covariates as well as some exogenous covariates. The proposed model includes several popular types of time series models as special cases and extends the functional coefficient autoregressive model and the classical regression and autoregressive mixed model. We propose a two-stage method to estimate the coefficients of the model, in which the first stage estimates all coefficients by the local linear method, and the second stage estimates constant coefficients using traditional ordinary least squares (OLS). Consistency and asymptotic normality of both the local linear estimators and two stage estimators are established under regularity conditions. Simulation studies are conducted to empirically examine the finite sample performance of the proposed method, and a real data example about Lake Shasta inflow is used to illustrate the application of the proposed model.

autoregressive model, linear regression, local linear, two-stage estimation, varying coefficient.

Received: September 11, 2023; Accepted: December 13, 2023; Published: January 2, 2024

How to cite this article: Zhiqiang Cao and Hui Li, Partially linear varying-coefficient autoregressive model, Advances and Applications in Statistics 91(2) (2024), 141-173. http://dx.doi.org/10.17654/0972361724011

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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