Generating Cycles in a Century of Prices 45 



The first step in the Schuster method of isolating 

 true periodicities by the method of the periodogram 

 consists in arranging the data of the statistical series 

 into groups of different lengths and then computing the 

 values of the coefficients of the sine tenns appropriate 

 to the different groups. The required lengths and 

 closeness of the groups are discussed * by Professor 

 Schuster, and he further shows how the probability 

 of the reality of any assumed cycle is dependent 

 upon the magnitude of the coefficient of its correspond- 

 ing harmonic in the periodogram. In brief, the prob- 

 ability of the reality of an assumed cycle is shown to 

 be dependent upon the relative size of A - where A is the 

 coefficient of the sine term descriptive of the assumed 

 cycle. 



Professor Turner's method, which he has called the 

 method of Fourier Sequence,^ is based upon Professor 

 Schuster's method of the periodogram. The device 

 may be illustrated by the problem in connection with 

 which the method of Fourier Sequence was developed. 

 In 1913, when Professor Turner published his essays, a 

 fairly good record of sunspots existed for a period of 156 

 years. His problem was to determine whether there 



1 See particularly "On the Periodicities of Sunspots," Philosophical 

 Transactions, A, vol. 206, p. 71. 



2 The fundamental memoirs of Professor Turner are "On the Har- 

 monic Analj'sis of Wolf's Sun-spot Numbers, With Special Reference to 

 Mr. Kimura's Paper," Monthly Notices of the Royal Astro?iomical 

 Society, May, 1913; "On the PJxpression of Sunspot Periodicity as a 

 Fourier Sequence, and on the General Use of a Fourier Sequence in 

 Similar Problems," i6id., 1913 (Supplement); " Further Remarks on the 

 Expression of Sun-spot Periodicity as a Fourier Sequence," ibid., 

 November, 1913. 



