Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models

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Facultad de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
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The problems of evaluating and maximizing the exact likelihood function of vector ARMA models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features which can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties offered by the evaluation algorithm, is also considered. Combining these two procedures, a new algorithm for exact maximum likelihood estimation of vector ARMA models is obtained. Comparisons with existing procedures, in terms of both analytical arguments and a numerical example, are given in order to show that the new estimation algorithm performs at least as well as existing ones, and that relevant real situations occur in which it do es better.
En este trabajo se estudian por separado los problemas asociados con la evaluación y la maximización de la función de verosimilitud exacta de modelos ARMA multivariantes. Por un lado, se diseña un nuevo algoritmo para evaluar dicha función eficientemente, que reúne una serie de propiedades que se encuentran por separado en los procedimientos actualmente disponibles. Por otro lado, se propone un mecanismo para maximizar la función de verosimilitud, que aprovecha las ventajas ofrecidas por el algoritmo de evaluación. Combinando ambos procedimientos, se obtiene un nuevo algoritmo de estimación por máxima verosimilitud exacta de modelos ARMA multivariantes, cuyo funcionamiento en la práctica resulta superior, en muchos aspectos, al de otros procedimientos alternativos.
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