Maximum likelihood estimators in linear regression models with Ornstein-Uhlenbeck process

Abstract

Abstract The paper studies the linear regression model y t = x t T β + ε t , t = 1 , 2 , … , n , where d ε t = λ ( μ − ε t ) d t + σ d B t , with parameters λ , σ ∈ R + , μ ∈ R and { B t , t ≥ 0 } the standard Brownian motion. Firstly, the maximum likelihood (ML) estimators of β, λ and σ 2 are given. Secondly, under general conditions, the asymptotic properties of the ML estimators are investigated. And then, limiting distributions for likelihood ratio test statistics of the hypothesis are also given. Lastly, the validity of the method are illuminated by two real examples. MSC:62J05, 62M10, 60J60.