On the vector-valued generalized autoregressive models

The classical autoregressive type models are widely used in time series modelling. Recently, a class of models known as generalized autoregressive, recognized by an additional parameter, has been proposed in order to reveal some hidden features which cannot be characterized by the standard autoregressive models. In this paper, the generalized autoregressive models are extended to the vector-valued autoregressive models which provide a flexible framework for modelling the dependent data. The properties of the new model such as stationary conditions, some explicit form of the auto-covariance function and the spectral density matrices are investigated. Unknown parameters are then estimated and compared with other kinds of traditional methods. The numerical results obtained by means of simulation studies are then reported. Finally, the traditional autoregressive model and generalized autoregressive model are fitted to a well-known bivariate time series, respectively, and the performance of the proposed models and the estimation methods are discussed.