Geodesic
Parameter Estimation in Linear Regression Models With Stationary Arma(p,q)-Errors Using Automatic Differentiation
Yugoslav journal of operations research, Tome 2 (1992) no. 1, p. 55 .

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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.
Keywords: time series, linear regression, automatic differentiation 
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     author = {Herbert Fischer and Stefan Schaffler and Hubert Warsitz},
     title = {Parameter {Estimation} in {Linear} {Regression} {Models} {With} {Stationary} {Arma(p,q)-Errors} {Using} {Automatic} {Differentiation}},
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Herbert Fischer; Stefan Schaffler; Hubert Warsitz. Parameter Estimation in Linear Regression Models With Stationary Arma(p,q)-Errors Using Automatic Differentiation. Yugoslav journal of operations research, Tome 2 (1992) no. 1, p. 55 . http://geodesic.mathdoc.fr/item/YJOR_1992_2_1_a4/