mHE economist is concerned with determining the and prospects of society. I In a more restricted, but nevertheless important, aspect of his work, he is concerned with determining the condition and prospects of business enterprise. The economist who is investigating problems relating to business is interested principally in the economic cycle, because our economic welfare is subject to the vagaries of this phenomenon. The data that exhibit economic cycles are of statistics. Methods for determining the correlation of are therefore fundamental to the investigation of economic cycles. The purpose of this paper is twofold. The first object is to describe a theory of correlation of that is particularly suited to determining the laws of economic cycles; the second is to introduce a practical application of the theory by means of a study of cycles in interest rates and in wholesale prices. Those wishing to obtain an idea of the theory here presented without going into the mathematics of the subject should limit their attention to Sections I, II, IV, VIII, and IX, on general theory, the correlation equation and the system factor, the economic indexes, forecasting, and the nature of the elements in the economic structure. Section III on solution for the system factor Y and, perhaDs. Darts of Section II will be of interest only to ose who may wish to apply the theory. Those interested in the practical results obtained by applying the method to a study of the relation between interest rates and wholesale prices will find Sections V, VI, and VII of primary interest. The type of statistical array called a series2 is one in which the items are ordered in a sequence that is fixed with respect to time. Annual, quarterly or monthly data of wholesale prices, interest rates, trade activity and rainfall are examples of important The difficulties encountered in applying the classic theory of correlation to are recognized by a number of statisticians. These difficulties are inherent in the problem, and are due to the fact that the fundamental propositions of random sampling do not apply to data that are definitely ordered with respect to time. We require, therefore, a more general theory, one that explicitly recognizes the possibility of mutual dependence between the successive items in the The essential idea of the theory proposed is that the correlation of presents a problem of multiple correlation, in which each item in one may depend upon not only the concurrent, but also upon the preceding, items in another The method of simple correlation, which is adequate for deducing the relation between of other types, is not sufficiently general to apply to series, because it considers only the relation between concurrent items in the series, and ignores the possible influence of preceding items. If, in a particular case, the preceding items are actually without influence, this fact can be demonstrated only by applying the more general theory. An intrinsic part of the theory is the concept of a system. Where two trains of events of different kinds are so related that each event of one kind exerts a definable effect upon the later events of the other kind, a systematic phenomenon is acting. A system is conceived to be an arrangement of connections and constraints 1When the Statistical Society of London was organized in I834, five years before the American Statistical Association, the prospectus announced that its functions were to 'procure, arrange and publish facts calculated to illustrate the condition and prospects of society' (presidential address by Warren M. Persons at the eighty-fifth annual meeting of the American Statistical Association). 2 The term is unfortunate, because, in mathematical usage, commonly refers to the sum of a number of quantities: thus, I+2+5+3, not I, 2, 5, 3. The data referred to as time series throughout the paper are sequtences of numbers that give the values of a variable at discrete, equally spaced intervals of time. They are, therefore, functions of time, in the way that function is understood in the calculus of finite differences. It has been suggested, therefore, (by Mr. John R. Carson of the American Telephone and Telegraph Company) that time sequences would be better than time series. The latter term is used so extensively in the literature of the subject, however, that I have refrained from introducing a new term.