Un algoritmo rápido para evaluar la función de verosimilitud exacta de modelos VARMAX periódicos

Abstract

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.