STATISTICIANS are familiar with the moving average. For example, when monthly prices are given, it may be desirable to eliminate the seasonal variation. The average of the monthly prices for a calendar year may be found, then the average of the prices from the February of this year to the January of the next, then from March to February, and so on. Each average thus formed involves just once each of the twelve months; and such averaging would seem a good method for eliminating the effects of the seasonal cycle. A question, however, arises: When we take out one cycle, such as the twelve-month cycle, are we likely to put in another cycle, with substantial waves? Under certain conditions, the answer is: Yes. But to understand why such an unwelcome cycle intrudes itself, some explanation is required. As a basis for studying cycles, it is often assumed that data contain an additive chance constituent. That is, it is assumed that the rth measurement Ur may be analyzed thus: