A new approach for time domain analysis of multivariate and functional time series

We apply the classical finite Fourier transform to construct an embedded functional process to a given multivariate time series model. The basic properties of the embedded functional process are presented. It appears that the embedded functional process is quite useful for the model building and prediction. We also provide a new method for approximating an infinite functional process with a finite functional process. The methodology is different from the classical one. Indeed, the active underlying frequencies are taken into consideration rather than the significant eigenvectors. The performance of our method is illustrated through simulations. Interestingly, in doing prediction, it appears that for our proposal the computation time is much shorter compared to existing ones.