g13bdf

Purpose

Synopsis

[wds,isf,ifail] = g13bdf(r0,r,nna,s<,ifail>)

Description

 
 The routine calculates estimates of parameters 
 (delta) ,(delta) ,...,(delta) , (omega) ,(omega) ,...,(omega)  in
        1        2            p         0        1            q 
 the transfer function model
 
 y =(delta) y   +(delta) y   +...+(delta) y   +(omega) x   
  t        1 t-1        2 t-2            p t-p        0 t-b
 
 -(omega) x     -...-(omega) x 
         1 t-b-1            q t-b-q
 
 given cross correlations between the series x  and lagged values 
                                              t                  
 of y :
     t
 
                       r  (l) , l=0,1,...,L
                        xy
 
 and the ratio of standard deviations s /s , as supplied by G13BCF.
                                       y  x                 
 
 It is assumed that the series x  used to calculate the cross 
                                t                            
 correlations is a sample from a time series with true 
 autocorrelations of zero. Otherwise the cross correlations 
 between the series b  and a , as defined in the description of 
                     t      t                                  
 G13BAF, should be used in place of those between y  and x .
                                                   t      t
 
 The estimates are obtained by solving for 
 (delta) ,(delta) ,...,(delta)  the equations
        1        2            p     
 
 r  (b+q+j)=(delta) r  (b+q+j-1)+...+(delta) r  (b+q+j-p) ,
  xy               1 xy                     p xy
 
 j=1,2,...,p
 
 
 then calculating
 
 (omega) =+-(s /s ){r  (b+i)-(delta) r  (b+i-1)-...
        i     y  x   xy             1 xy           
 
                    -(delta) r  (b+i-p)} ,       i=0,1,...,q
                            p xy
 
 where the '+' is used for (omega)  and '-' for (omega) , i>0.
                                  0                    i     
 
 Any value of r  (l) arising in these equations for l<b is taken 
               xy                                               
 as zero. The parameters (delta) ,(delta) ,...,(delta)  are 
                                1        2            p    
 checked as to whether they satisfy the stability criterion.
 

Parameters

g13bdf

Required Input Arguments:

r0                                    real
r (:)                                 real
nna (3)                               integer
s                                     real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

wds (:)                               real
isf (2)                               integer
ifail                                 integer