Generating Cycles in a Century of Prices 47 



An Analysis of a Century of Prices 



As a preliminary step our investigation will follow 

 the method of Professor Turner in the analysis of 

 Sauerbeck's index numbers of general wholesale prices. 



Sauerbeck's index numbers of general wholesale 

 prices from 1818 to 1913 are recorded in Table I of the 

 Appendix and are graphed in Figure 11. The graph 

 shows quite clearly that the mean value of the items in 

 the early part of the series is higher than the mean 

 value during the latter part, and we are, therefore, 

 confronted with the question as to what shall be done 

 about the secular trend of the figures. Any hypothesis 

 that might be made as to the type of curve to represent 

 the secular trend would, to a degree, be an arbitrary 

 hypothesis, and my decision has been to make no 

 supposition as to the secular trend, but to proceed with 

 the computation of the Fourier tenns from the crude 

 index numbers. In support of this decision these two 

 considerations are offered: 



1. It is known that each term of a Fourier sequence is 

 independent of the other tenns, and there is, therefore, a 

 probability that when a Fourier series is fitted to the 

 statistical data covering a considerable length of time, 

 the early tenns of the series will make an allowance for 

 the secular trend which will be independent of the later 

 terms. ^ Figures 11, 12, 13, 14 show the reasonable- 



1 Cf . Schuster, "The Periodogram of Magnetic Dedination," p. 113. 

 "Table . . . clearly shows the effects of secular variation, and we 

 must consider in how far it is necessary to take any notice of this 

 variation. If our observations extended over an indefinite time, 

 Fourier's analysis would itself perfonn all that is required, and each 

 period would be totally independent of all others." 



