where A^^i^ and B^i, are the k"^ Fourier cosine and sine coefficients, respec- 

 tively, of time series x^ . Similarly, the second time series can be 

 expressed in the form 



V L r 27r(k - l)(n - 1) 1 



. r2 7r(k - l)(n - 1)1 1 10 N 

 + Byk sinj^-^ ^ -\\ n=l, 2, ...,2 (22) 



where Ay^ and By^ are the k*"^ Fourier cosine and sine coefficients, respec- 

 tively, of time series y„ . The Fourier coefficients can be found from the 

 time series points through the formulae 



A.1 = J ?: x„ (23) 



^^ n=l 



2 ?, r 27r(k - l)(n - 1) ] ,0-5 ^ 

 A.. = ^K^nCos k=2, 3, ...,2 (24) 



2 ?- . r 27r(k - l)(n - 1) ] , . ^ 



= N J, ^ 'H ^ J k = 2, 3, 



for time series x„ , and the formulae 



1 " 



2 ?, r 27r(k - l)(n - 1)1 , „ , 



V - N 1 y- ^°n ^ J ^=2,3, 



N 

 ' 2 



N 

 ' 2 



2 f . r 27r(k - l)(n - 1) 1 u 9 . N 



for time series y^^ . 



(25) 



(26) 



(27) 



(28) 



By, = (29) 



(30) 



15 



