Decomposition of the multi-dimensional time series identification problem

The mathematical model of shaping filter is constructed for a stationary multidimensional time series. The identification procedure is simplified by dividing into several steps: each step results in a multidimensional filter such that the autocovariance generating function of the transformed time series has nonzero entries in only one row, one column and in the main diagonal. This decomposition allows to construct adequat models containing relatively small number of estimated parameters. The reasonable parametrizaion, in turn, contributes to the better quality of the model due to the better statistical accuracy of the parameter estimations.