Language Reference: VTSROOT Call

VTSROOT Call

CALL VTSROOT( root, phi, theta <, p> <, q> ) ;

The VTSROOT subroutine computes the characteristic roots of the model from AR and MA characteristic functions.

The input arguments to the VTSROOT subroutine are as follows:

phi: specifies a $\text{[math]}$ matrix that contains the autoregressive coefficient matrices, where $\text{[math]}$ is the number of the elements in the subset of the AR order and $\text{[math]}$ is the number of variables. You must specify either phi or theta.
theta: specifies a $\text{[math]}$ matrix that contains the moving average coefficient matrices, where $\text{[math]}$ is the number of the elements in the subset of the MA order. You must specify either phi or theta.
p: specifies the subset of the AR order. See the VARMACOV subroutine.
q: specifies the subset of the MA order. See the VARMACOV subroutine.

The VTSROOT subroutine returns the following value:

root

is a $\text{[math]}$ matrix, where $\text{[math]}$ is the maximum order of the AR characteristic function and $\text{[math]}$ is the maximum order of the MA characteristic function. The first $\text{[math]}$ rows refer to the results of the AR characteristic function; the last $\text{[math]}$ rows refer to the results of the MA characteristic function.

The first column contains the real parts, $\text{[math]}$ , of eigenvalues of companion matrix associated with the AR( $\text{[math]}$ ) or MA( $\text{[math]}$ ) characteristic function; the second column contains the imaginary parts, $\text{[math]}$ , of the eigenvalues; the third column contains the moduli of the eigenvalues, $\text{[math]}$ ; the fourth column contains the arguments ( $\text{[math]}$ ) of the eigenvalues, measured in radians from the positive real axis. The fifth column contains the arguments expressed in degrees rather than radians.

Consider the roots of the characteristic functions, $\text{[math]}$ and $\text{[math]}$ , where $\text{[math]}$ is an identity matrix with dimension 2 and

$\text{[math]}$

To compute these roots, you can use the following statements:

  phi  = { 1.2 -0.5, 0.6 0.3 };
  theta= {-0.6  0.3, 0.3 0.6 };
  call vtsroot(root, phi, theta);