g13ahf

Purpose

Synopsis

[fva,fsd,ifail] = g13ahf(st,mr,par,c,rms,nfv<,ifail>)

Description

 
 The original time series is x , for t=1,2,...,n and parameters 
                              t                                
 have been fitted to the model of this time series using G13AFF.
 
 Forecasts of x , for t=n+1,n+2,...,n+L, are calculated in five 
               t                                               
 stages, as follows:
 
 (i)   set a =0 for t=N+1,N+2,...,N+L, where N=n-d-(D*s) is the 
            t                                                  
       number of differenced values in the series,
 
 (ii)  calculate the values of e  for t=N+1,N+2,...,N+L, where 
                                t                             
       e =(phi) *e   +...+(phi) *e   +a -(theta) *a   -...
        t      1  t-1          p  t-p  t        1  t-1   
  
          -(theta) *a   ,
                  q  t-q
 
 (iii) calculate the values of w  for t=N+1,N+2,...,N+L, where 
                                t                             
       w =(Phi) *w   +...+(Phi) *w     +e -(Theta) *e   -...
        t      1  t-s          P  t-s*P  t        1  t-s    
 
          -(Theta) *e     ,
                  Q  t-s*Q
 
       where w  for t<=N are the first s*P values in the state 
                t                                               
       set, corrected for the constant,
 
 (iv)  add the constant term c to give the differenced series 
              d       D                             
       (nabla) (nabla) x =w +c for t=N+1,N+2,...,N+L,
                      s t  t                        
 
 (v)   the differencing operations are reversed to reconstitute x 
                                                                 t
       for t=n+1,n+2,...n+L.
 
 The standard errors of these forecasts are given by 
             2      2          2      1/2                       
 s ={V*((psi) +(psi) +...+(psi)     )}    for t=n+1,n+2,...,n+L, 
  t          0      1          t-n-1                            
 where (psi) =1, V is the residual variance of a  and (psi)  is 
            0                                   t          j   
 the coefficient expressing the dependence of x  on a   .
                                               t     t-j
 
 To calculate (psi)  for j=1,2,...,(L-1) the following device is 
                   j                                            
 used.
 
 A copy of the state set is initialised to zero throughout and the
 calculations outlined above for the construction of forecasts are
 carried out with the settings a   =1, and a =0 for 
                                N+1         t      
 t=N+2,N+3,...,N+L.
 
 The resulting quantities corresponding to the sequence 
 x   ,x   ,...,x    are precisely 1, (psi) ,(psi) ,...,(psi)   .
  N+1  N+2      N+L                       1      2          L-1
 
 The supplied time series model is used throughout these 
 calculations, with the exception that the constant term c is 
 taken to be zero.
 

Parameters

g13ahf

Required Input Arguments:

st (:)                                real
mr (7)                                integer
par (:)                               real
c                                     real
rms                                   real
nfv                                   integer

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

fva (nfv)                             real
fsd (nfv)                             real
ifail                                 integer