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Linear transformations of vector ARMA processes. (English) Zbl 0555.62072
Linear transformations of stochastic processes are used in many ways in economic analyses, for example when linear aggregates or subprocesses are considered. It is demonstrated that a linear transformation of a vector ARMA process is again an ARMA process and conditions for stationarity are given. Three different predictors for a linearly transformed process are compared. Forecasting the original process and transforming the predictions is superior to forecasting the transformed process directly and to transforming univariate predictions of the components of the original process. Conditions for equality of the three different forecasts are provided.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
62P20 Applications of statistics to economics
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