Language Reference
VTSROOT Call
CALL VTSROOT (root, phi, theta <, p> <, q> ) ;
This subroutine is supported by the IML procedure and the iml action.
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
matrix that contains the autoregressive coefficient matrices, where 
is the number of the elements in the subset of the AR order and 
is the number of variables. You must specify either phi or theta. - theta
specifies a
matrix that contains the moving average coefficient matrices, where 
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
matrix, where 
is the maximum order of the AR characteristic function and 
is the maximum order of the MA characteristic function. The first 
rows refer to the results of the AR characteristic function; the last 
rows refer to the results of the MA characteristic function. The first column contains the real parts, x, of eigenvalues of companion matrix associated with the AR(
) or MA() characteristic function; the second column contains the imaginary parts, y, of the eigenvalues; the third column contains the moduli of the eigenvalues, 
; the fourth column contains the arguments (
) 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, 
and 
, where I is an identity matrix with dimension 2 and
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);
cols = {"Real" "Imag" "Modulus" "Radians" "Degrees"};
print root[colname=cols];
Figure 494: Characteristic Roots
| root | ||||
|---|---|---|---|---|
| Real | Imag | Modulus | Radians | Degrees |
| 0.75 | 0.3122499 | 0.8124038 | 0.3945069 | 22.603583 |
| 0.75 | -0.31225 | 0.8124038 | -0.394507 | -22.60358 |
| 0.6708204 | 0 | 0.6708204 | 0 | 0 |
| -0.67082 | 0 | 0.6708204 | 3.1415927 | 180 |