Parameter Estimation in Linear Regression Models With Stationary Arma(p,q)-Errors Using Automatic Differentiation


Herbert Fischer, Stefan Schaffler, Hubert Warsitz




The use of Automatic Differentiation for Time Series Analysis is considered. Especially we discuss the exact. ML-estimation for linear regression models with stationary ARMA(p,q) residuals. The gradient and the Hessian matrix of the likelihood function, which has to be minimized, can be computed at fixed bur arbitrary chosen points by Automatic Differentiation. The stationary region for the ARMA(p,q) residuals is represented as a system of nonlinear inequalities. The special behavior of the likelihood function allows to use well-known methods for solving unconstrained nonlinear programming problems.