Although it is possible to study time series analysis without explicit use of Hilbert space terminology and techniques, there are great advantages to be gained from a Hilbert space formulation. These are largely derived from our familiarity with two- and three-dimensional Euclidean geometry and in particular with the concepts of orthogonality and orthogonal projections in these spaces. These concepts, appropriately extended to infinite-dimensional Hilbert spaces, play a central role in the study of random variables with finite second moments and especially in the theory of prediction of stationary processes.
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