Language Reference
VARMALIK Call
CALL VARMALIK (lnl, series, phi, theta, sigma <, p> <, q> <, opt> ) ;
This subroutine is supported by the IML procedure and the iml action.
The VARMALIK subroutine computes the log-likelihood function for a VARMA(
) model.
The input arguments to the VARMALIK subroutine are as follows:
- series
specifies an
matrix that contains the vector time series (assuming mean zero), where n is the number of observations and 
is the number of variables. - phi
specifies a
matrix that contains the autoregressive coefficient matrices, where 
is the number of the elements in the subset of the AR order. 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. - sigma
specifies a
covariance matrix of the innovation series. If you do not specify sigma, an identity matrix is used. - p
specifies the subset of the AR order. See the VARMACOV subroutine.
- q
specifies the subset of the MA order. See the VARMACOV subroutine.
- opt
-
specifies the method of computing the log-likelihood function:
- opt=0
requests the multivariate innovations algorithm. This algorithm requires that the time series is stationary and does not contain missing observations.
- opt=1
requests the conditional log-likelihood function. This algorithm requires that the number of the observations in the time series must be greater than p
q and that the series does not contain missing observations. - opt=2
requests the Kalman filtering algorithm. This is the default and is used if the required conditions in opt=0 and opt=1 are not satisfied.
The VARMALIK subroutine returns the following value:
- lnl
is a
matrix that contains the log-likelihood function, the sum of log determinant of the innovation variance, and the weighted sum of squares of residuals. The log-likelihood function is computed as 
(the sum of last two terms).
The options opt=0 and opt=2 are equivalent for stationary time series without missing values. Setting opt=0 is useful for a small number of the observations and a high order of p and q; opt=1 is useful for a high order of P and q; opt=2 is useful for a low order of p and q, or for missing values in the observations.
Consider the following bivariate (
) VARMA(1,1) model:
To compute the log-likelihood function of this model, you can use the following statements:
phi = { 1.2 -0.5, 0.6 0.3 };
theta= {-0.6 0.3, 0.3 0.6 };
sigma= { 1.0 0.5, 0.5 1.25};
call varmasim(yt, phi, theta) sigma=sigma seed=123;
call varmalik(lnl, yt, phi, theta, sigma);
labl = {"LogLik", "SumLogDet", "SSE"};
print lnl[rowname=labl];
Figure 490: Log-Likelihood Components
| lnl | |
|---|---|
| LogLik | -85.50804 |
| SumLogDet | 4.8529601 |
| SSE | 166.16313 |