It has several times been noted that time series commonly possess in many respects the characteristics of series of cumulated random numbers. The separate items in such time series are by no means random in character, but the changes between successive items tend to be largely random. This characteristic has been noted conspicuously in sensitive commodity prices. On the basis of the differences between chain and fixed-base index numbers King has concluded that stock prices resemble cumulations of purely random changes even more strongly than do commodity prices.

The fact that series commonly used as indexes of business activity closely resemble series obtainable by cumulating random numbers has given support to the theory that so-called business cycles result in large degree from cumulative effects of independent random influences bearing on the business situation – some favourably, some unfavourably.

In the discussion which follows, a series such as may be obtained by cumulating random numbers will for brevity and clarity be called usually a random-difference series, since it is the first differences of the series and not the items of the series itself which are random. The natural alternative term of cumulated random series is subject to misinterpretation as describing a series that is itself random.

Economic theory has fallen far short of recognizing the full implications of the resemblance of many economic time series to random-difference series; and methods of statistical analysis in general use have given these implications virtually no recognition.