Time Series: Theory and Methods pp 159-190 | Cite as
Prediction of Stationary Processes
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.)
Keywords
Stationary Process Prediction Error Linear Predictor Orthogonal Subspace Autocovariance FunctionPreview
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