Publication: Un algoritmo rápido para evaluar la función de verosimilitud exacta de modelos VARMAX periódicos
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1998
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Facultad de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
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Abstract
En este trabajo se deriva un algoritmo rápido para evaluar la función de verosimilitud exacta de procesos VARMAX periódicos. Su eficiencia computacional se consigue combinando una formulación de dimensión mínima en espacio de los estados, en forma steady-state innovations y un procedimiento para evaluar la función de verosimilitud exacta que aprovecha las propiedades de esta representación. El algoritmo es aplicable a modelos estacionarios y no estacionarios, con variables exógenas estocásticas y/o deterministas y facilita el cálculo de los segundos momentos exactos de las estimaciones. Por otra parte, la representación utilizada permite tratar casos no considerados en la literatura, como procesos periódicos multivariantes, y admite estructuras dinámicas no homogéneas y muestras con distinto número de observaciones en cada estación. Asimismo, es inmediatamente aplicable a cualquier caso de variación paramétrica determinista. Algunas pruebas con datos simulados ponen de manifiesto el buen funcionamiento del algoritmo.
In this work we derive a fast algorithm to compute the exact likelibood function of periodic VARMAX processes. Its computational efficiency is achieved by combining a minimal dimension state-space formulation, in steady-state innovations form, and a procedure for computing the exact likelihood function which takes advantage of the properties of this representation. The algorithm can be applied to stationary and non-stationary models, allows for deterministic and/or stochastic exogenous variables and makes easy the computation of the exact second-order moments of the estimates. On the other hand, our approach includes representations not considered by the literature, like multivariate periodic processes, and allows for nonhomogeneous dynamic structures and different number of observations in each season. Besides, it can be applied to any model with deterministic parameter variation. Some results with simulated data illustrate the good behaviour of the algorithm.
In this work we derive a fast algorithm to compute the exact likelibood function of periodic VARMAX processes. Its computational efficiency is achieved by combining a minimal dimension state-space formulation, in steady-state innovations form, and a procedure for computing the exact likelihood function which takes advantage of the properties of this representation. The algorithm can be applied to stationary and non-stationary models, allows for deterministic and/or stochastic exogenous variables and makes easy the computation of the exact second-order moments of the estimates. On the other hand, our approach includes representations not considered by the literature, like multivariate periodic processes, and allows for nonhomogeneous dynamic structures and different number of observations in each season. Besides, it can be applied to any model with deterministic parameter variation. Some results with simulated data illustrate the good behaviour of the algorithm.
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