Introduction 5 



secular, cyclical, and random elements. The term 

 cycle is mathematically defined with definite period, 

 amplitude, and phase. The primary object of the 

 theory is not to forecast but to establish the existence 

 of real cycles and to trace the causes of the specifically 

 cyclical elements in the total of economic changes. It 

 distinguishes between a rational forecast and an empir- 

 ical forecast. No rational forecast can be made until 

 the manner of change in the various constituents of the 

 full cause is discovered and their measured interrelations 

 are known. Empirical forecasts of value may be made, 

 and are made, from the known routine in the sequence 

 of economic changes. 



Method and Results 



If the third type of theory with regard to the nature 

 of cjTles is allowed, then one is confronted with the 

 problem of finding a method of detennining whether a 

 series of observations contains real cycles. Several 

 technical methods, to which reference will be made in 

 the following chapters, have been devised for this pur- 

 pose; but without entering upon technicalities we may 

 see that from the point of view of forecasting and con- 

 trolling economic changes, the importance of a cycle is 

 dependent upon its amplitude. A cycle may be real 

 and yet practically negligible if its recurrent effects are 

 small. This very practical consideration suggests the 

 method to adopt in order to discover significant cycles. 

 It is obvious that whatever may be the mathematical 

 justification of the procedure it is practically important 

 to know which cycle will show the largest amplitude in 



