44 Generating Economic Cycles 



values of the original data? If, for example, a high 

 value were obtained for one of the A-coefficients in the 

 sine series, what warrant would there be for assuming 

 that the particular sine term of which the given A was 

 the coefficient would be significant of a real recurring 

 periodicity? 



This problem was considered by Professor Schuster 

 in his theory of the periodogram.^ According to Profes- 

 sor Schuster, "the periodogram may be said to put the 

 statistical material in a fonn in which it may be most 

 readily discussed, but there may be always cases in 

 which the interpretation is difficult. ... I do not, of 

 course, claim to have first introduced the application 

 of Fourier's Theorem to the discovery of hidden 

 periodicities. . . . The process is sufficiently obvious to 

 have been frequently introduced, but it has generally 

 been assumed that each maximum in the amplitude of a 

 harmonic term corresponded to a true periodicity. 

 What distinguishes the method which I am endeavour- 

 ing to introduce from that of others, is the discussion 

 of the natural variability of the Fourier coefficients 

 according to the theory of probability, independently 

 of any periodic cause which may have influenced the 

 phenomenon." ^ 



1 The fundamental memoirs of Professor Schuster are: 



"On the Investigation of Hidden Periodicities with Application to a 

 Supposed 26 Day Period of Meteorological Phenomena," Terrestrial 

 Magnetism, for March, 1898; "The Periodogram of IMagnetic Declina- 

 tion as Obtained from the Records of the Greenwich Observatory during 

 the Years 1871-1895," Cambridge Philosophical Society Transactions, 

 vol. 18, 1899; "On the Periodicity of Sunspots," Philosophical Transac- 

 tions of the Royal Society of London, A, vol. 206, 1906. 



2 "On the Periodicities of Sunspots," Philosophical Transactions, A, 

 vol. 206, pp. 71, 72. 



