QML estimators in linear regression models with functional coefficient autoregressive processes (Q980670)

Summary: This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of \textit{R. A. Maller} [Stochastic Processes Appl. 105, No. 1, 33--67(2003; Zbl 1075.60507)], \textit{J. S. White} [Ann. Math. Stat. 30, 831--834 (1959; Zbl 0133.42403)], \textit{P. J. Brockwell} and \textit{R. A. Davis} [Time series: theory and methods. NY: Springer (1987; Zbl 0604.62083)], and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.