By using the classical finite Fourier transform,we construct a functional process to a given multivariate time series model. The basic properties of this functional process are presented. We found that the functional process is suitable for the model building and prediction. There are interesting relation between the multivariate time series models and new functional process models. Also the models operators are specified and extracted from the multivariate coefficients matrices. We also provide a new method for approximating an infinite functional process with a finite functional process. The method is something different from the traditional one, and active frequencies are taken into consideration rather than the significant eigenvectors. Finite approximation by new method seems to decrease the calculation time. We also make a comparison between the Bosq finite process and our functional process prediction errors.
