18 Economic Cycles: Their Law and Cause 



constant recurrence of the cycles may place one in a 

 position to foresee and utilize the dependent phenomena. 

 But the control of phenomena dependent upon a cycle 

 presupposes that the cycle is itself a real phenomenon 

 with a natural cause, and that consequently it persists 

 with an increase in the number of observations. If, 

 however, an apparent cycle of any length taken at 

 random is obtained from the given data, one would 

 surely misspend his time if he were to set about the 

 search for its cause, and were to derive conclusions based 

 upon the hypothesis of the persistence of the cause. 

 The cycles due to formal, accidental causes must be 

 discriminated from the cycles with natural causes. 



The separation of true cycles from spurious or 

 accidental cycles is facilitated by the periodogram l of 

 observations. If, following Professor Schuster, we call 

 the square of the amplitude of any given period the 

 "intensity" of the period, then it may be said that the 

 probability of the reality of a period is dependent upon 

 the ratio of its intensity to the mean intensity of the 

 periodogram. Or, again following Professor Schuster, 

 if we call the mean intensity of the periodogram the 

 "expectancy," then the reality of a period is dependent 

 upon the ratio of its intensity to the expectancy of the 

 periodogram. For instance, if in case of a given period 

 the ratio of intensity to expectancy is, say, 3 to 1, then 

 in about one case in twenty we should expect to obtain 

 by chance a greater amplitude than the amplitude of 

 the particular period in question. If, on the other hand, 



1 See the preceding note. 



