The solution to the problem of optimal linear forecasting the stationary stochastic process via the known trend is obtained. It is shown that this solution provides solving the problem of linear forecasting via an unknown trend if the linear forecast of the trend is replaced by its optimal linear estimator. The relation between errors of forecasting via known and unknown trend is found. Strong influence of the decorrelation effect on the forecast error is illustrated. Recommendations for designing practical forecasting algorithms are obtained.
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