In time series analysis there are two lines of approach, here called the functional and the stochastic. In the former case, the given time series is interpreted as a mathematical function, in the latter case as a random specimen out of a universe of mathematical functions. The close relation between the two approaches is in section 2 shown to amount to a genuine isomorphism. Considering the problem of prediction from this viewpoint, the author gives in sections 3-4 the functional equivalence of his earlier theorem on the decomposition of a stationary stochastic process with a discrete time parameter (see [9], theorem 7). In section 5 the decomposition theorem is applied to the problem of linear prediction. Finally in section 6 a few comments are made. Since various aspects of the isomorphism in question are known, this paper might be regarded as essentially expository.