Method of retrospective prediction as applied to predicting the trend of a steady random process

An effective algorithm of predicting the trend (deterministic basis) m(t) of a steady (in a wide sense) random process X(t) is proposed. The initial information about the random process X(t) is limited to the assumption that its mean value (mathematical expectation) is equal to zero. The interval [0, T] of observation of the trend sum m(t) and the sample x(t) of the random process X(t) is assumed to be finite. Construction of a prediction estimate µ(T +τ), where τ is the prediction interval, ensures automatic allowance for statistical characteristics of the random process X(t).