Time Series and Harmonic Analysis

Although many articles on the present subject have appeared in the mathematical, statistical, and physical literature, there still seems to be some justification for one more. The statisticians have applied only small parts of the theory; the physicists have gone deeper, but write like physicists; the mathematicians have gone furthest, but write like mathematicians, only for posterity. Their work is frequently not understood, and is in general either ignored or applied in simplified forms which often are formally more formidable than the original rigorous one. The present paper attempts to give a compact outline of the harmonic analysis of stochastic processes, with applications to physical problems.* Time series can be analysed from two points of view.