Displaying similar documents to “On extrapolation in multiple ARMA processes”

Improvement of prediction for a larger number of steps in discrete stationary processes

Tomáš Cipra (1982)

Aplikace matematiky

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Let { W t } = { ( X t ' ' , Y t ' ) ' } be vector ARMA ( m , n ) processes. Denote by X ^ t ( a ) the predictor of X t based on X t - a , X t - a - 1 , ... and by X ^ t ( a , b ) the predictor of X t based on X t - a , X t - a - 1 , ... , Y t - b , Y t - b - 1 , ... . The accuracy of the predictors is measured by Δ X ( a ) = E [ X t - X ^ t ( a ) ] [ X t - X ^ t ( a ) ] ' and Δ X ( a , b ) = E [ X t - X ^ t ( a , b ) ] [ X t - X ^ t ( a , b ) ] ' . A general sufficient condition for the equality Δ X ( a ) = Δ X ( a , a ) ] is given in the paper and it is shown that the equality Δ X ( 1 ) = Δ X ( 1 , 1 ) ] implies Δ X ( a ) = Δ X ( a , a ) ] for all natural numbers a .