g13bcf

Purpose

Synopsis

[s,r0,r,stat,ifail] = g13bcf(x,y,nl<,ifail>)

Description

 
 Given two series x ,x ,...,x  and y ,y ,...,y  the routine 
                   1  2      n      1  2      n            
 calculates the cross correlations between x  and lagged values of
                                            t                   
 y :
  t
                      n-l              
                      --     _       _ 
                      >  (x -x)(y   -y)
                      --   t     t+l   
                      t=1              
             r  (l)= ------------------ , l=0,1,...,L
              xy           ns s        
                             x y       
 
 where
 
                                 n   
                                 --  
                                 >  x 
                                 --  t
                             _   t=1 
                             x= ------
                                  n
 
                               n        
                               --     _ 2
                               >  (x -x) 
                               --   t   
                           x   t=1      
                          s = -----------
                                   n
 
 and similarly for y.
 
 The ratio of standard deviations s /s  is also returned, and a 
                                   y  x                        
 portmanteau statistic is calculated:
 
                               L         
                               --       2
                        STAT=n >  r  (l) .
                               --  xy    
                               i=1       
 
 Provided n is large, L much less than n, and both x ,y  are 
                                                    t  t    
 samples of series whose true autocorrelation functions are zero, 
 then, under the null hypothesis that the true cross correlations 
                                              2                  
 between the series are zero, STAT has a (chi)  distribution with 
 L degrees of freedom. Values of STAT in the upper tail of this 
 distribution provide evidence against the null hypothesis.
 

Parameters

g13bcf

Required Input Arguments:

x (:)                                 real
y (:)                                 real
nl                                    integer

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

s                                     real
r0                                    real
r (nl)                                real
stat                                  real
ifail                                 integer