Vector ARMA Models



The ZIP file contains the following files:

    vecarma.dll
    vecarma.lcg
    vecarma.src
    vecarma.e
    compx.dat
    compx.out


The material in these files are in the public domain.  And while the
author disclaims any responsibility for the performance of this
software, he would appreciate receiving any comments.


Ron Schoenberg
rons@Aptech.com

June 21, 2000




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                             vecarma.e


Copy this file to the GAUSSHOME\examples subdirectory.


This example file estimates the parameters of VARMA models using the
Constrained Maximum Likelihood (CML) application module.   If the
time series is multivariate it first estimates a series of univariate
models for start values.  It assumes Normally distributed errors.

This implementation also places the following constraints on the
parameters, first, it constrains the residuals covariance matrix
to be positive definite, and second, the roots of the determinantal
equations

    det(I - AR_1 t - AR_2 t^2 - ... )
    det(I + MA_1 t + MA_2 t^2 + ... )

to be outside the unit circle.







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                             compx.dat


Copy this file to the GAUSSHOME\examples subdirectory.

This file contains the close, overnight, and day movements in the
NASDAQ COMP index from Jan 8, 1999 through Jan 5, 2000.  It is
used by vecarma.e.







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                             compx.out


This file is the output from the execution of vecarma.e.










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                             vecarma.src


Copy this file to the GAUSSHOME\src subdirectory.

This contains GAUSS source code implementing the VARMA DLL.  It contains
two functions, one that returns the Normal log-likelihood function and
the other that returns the computed residuals:

/*
**> vecarmall
**
**  Purpose:  computes Vector ARMA Normal log-likelihood
**
**  Format:   ll = vecarmall(w,phi,theta,Q);
**
**  Input:    w         NxK matrix, time series
**
**            phi       K*PxK matrix, AR coefficient matrices
**
**            theta     K*QxK matrix, MA coefficient matrices
**
**            Q         KxK symmetric matrix, residual covariance matrix
**
**  Output:   LL        scalar, value of log-likelihood
*/


/*
**> vecarmares
**
**  Purpose:  computes Vector ARMA log-likelihood
**
**  Format:   res = vecarmares(w,phi,theta,Q);
**
**  Input:    w         NxK matrix, time series
**
**            phi       K*PxK matrix, AR coefficient matrices
**
**            theta     K*QxK matrix, MA coefficient matrices
**
**            Q         KxK symmetric matrix, residual covariance matrix
**
**
**  Output:   res       NxK matrix, residuals.
*/



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                             vecarma.lcg


Copy this file to the GAUSSHOME\lib subdirectory.


This is the library file.  Alternatively, enter the following command
from GAUSS:

    lib -u -a gauss vecarma.src

This will add vecarma.src and its procedure names to the gauss.lcg
library file.  When this is done you won't need to add the library vecarma
to your command files.









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                             vecarma.dll


Copy this file to the GAUSSHOME\dlib subdirectory


This dll is a compilation of source code produced by Jose Alberto
Mauricio of the  Universidad Complutense de Madrid.  It was published
as Algorithm AS311 in Applied Statistics.  Also described in "Exact
maximum likelihood estimation of stationary vector ARMA models, JASA,
90:282-264.

The following describes the arguments in the call to vecarmadll:

  dllcall
vecarmadll(m,p,q,n,w,phi,theta,qq,atf,a,sigma2,xitol,logelf,f1,f2,retcode);

         m        scalar, number of time series
         p        scalar, number of AR lags
         q        scalar, number of MA lags
         n        scalar, length of series
         w        nxm matrix, time series
         phi      p*m+1xm matrix, AR parameters
         theta    q*m+1xm matrix, MA parameters
         qq       mxm matrix, covariance matrix
         atf      scalar, set to 1 for calculation of residuals, else 0
         a        nxm matrix, residuals if atf = 1
         sigma2   scalar, value of sigma squared
         xitol    scalar, set to negative value for exact log-likelihood,
                   else set to tolerance
         logelf   scalar, on output set to value of log-likelihood
         f1       scalar, value of quadratic form (equation 2 in AS 311 paper)
         f2       scalar, det(Q)^n times the determinant of I+M'H'HM
         retcode  scalar, return code

                0    normal return
                1    M < 1
                2    N < 1
                3    P < 0
                4    Q < 0
                5    P = 0 and Q = 0
                7    floating point work space too small
                8    integer work space too small
                9    qq is not positive definite
               10    AR parameters too close to stationarity boundary
               11    model not stationary
               12    model not invertible
               13    I+M'H'HM not positive definite