On improvement of prediction in arma processes

Abstract

Necessary and sufficient conditions are derived in the paper that enable to decide whether an additional multivariate process will improve the prediction in a given multivariate discrete stationary process. The both processes are assumed to form together a process ARMAm n Further it was investigated wnen one can asser t that the both processes are uncorrelated provided the additional process did not improve the prediction in the original process, Some hints for the actual construction of predictors in a multivariate ARMA. (m n) process can be found in the paper.