Estimation and variable selection for partially linear functional-coefficient autoregressive errors-in-variables models

In many disciplines, particularly economics and finance, data are often contaminated by measurement errors while exhibiting autoregressive dependence, which complicates estimation and inference. This paper introduces a partially linear functional-coefficient autoregressive errors-in-variables model that simultaneously captures the dynamic persistence of past observations and the linear effects of covariates. The data are assumed to be stationary and α-mixing. We develop a bias-corrected profile least-squares method to estimate both the nonparametric coefficient functions and the regression parameters, and establish the asymptotic normality of the resulting estimators under mild conditions. To guard against potential overfitting from spurious covariates in the linear component, we further propose a bias-corrected penalised profile least-squares procedure with a smoothly clipped absolute deviation (SCAD) penalty, and show that the regularised estimators possess the oracle property. Extensive simulations and an empirical analysis of the Istanbul Stock Exchange dataset demonstrate the finite-sample performance and practical utility of the proposed methods.