Generating Cycles in a Century of Prices 51 



Fourier constituents. Table II shows that not only are 

 the values of ^- large for the period between 24 and 16 

 years, and for the period between 8.7 and 7.4 years, 

 but that in both instances there is a change of sign in 

 either a or 6. 



Considering that in a record of 96 years a possible 

 cycle of about 16 years could occur six times and one of 

 about 8 years could occur twelve times, this analysis of 

 a century of prices seems to warrant the conclusion that 

 there may be a real cycle of prices between 16 and 24 

 years in length, and that there is a large probability of 

 the existence of a real cycle in the neighborhood of 8 

 years. As the argument proceeds we shall have strong 

 additional reason for believing that the indicated 

 eight-year cycle in the Sauerbeck index numbers of 

 wholesale prices is a real cycle with an assignable 

 cause. Certainly the Fourier analysis indicates that if 

 there is a real cycle in the 96 years of the Sauerbeck 

 observations, its most probable value is in the neighbor- 

 hood of eight years. 



In order to isolate and exhibit the cycles of approxi- 

 mately eight years the graphs of Figures 13, 14, 15 

 have been computed and drawn. Figure 13 shows the 

 Fourier constituent of 19.2 years — which, according to 

 Table II, is one of the most important constituents — 

 and the compound curve that results from combining 

 the mean of the Sauerbeck observations with the Fourier 

 constituents of 96, 48, and 19.2 years. Figure 14 depicts 

 the 16-year Fourier constituent and the compound 

 curve made up of the mean value of the Sauerbeck 

 nmnbers and the 96-, 48-, 19.2- and 16-year Fourier 

 constituents. A re\dew of Figures 11, 12, 13, 14 



