Abstract
In this chapter we investigate the problem of predicting the values {X t , t ≥ n + 1} of astationary process in terms of {X 1,..., X n }. Theideais to utilize observations taken at or before time n to forecast the subsequent behaviour of {X t }. Given any closed subspace M of L 2(Ω, F, P), the best predictor in M of X n+h is defined to be the element of M with minimum mean-square distance from X n+h This of course is not the only possible definition of “best”, but for processes with finite second moments it leads to a theory of prediction which is simple, elegant and useful in practice. (In Chapter 12 we shall introduce alternative criteria which are needed for the prediction of processes with infinite second-order moments.)KeywordsStationary ProcessPrediction ErrorLinear PredictorOrthogonal SubspaceAutocovariance FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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