The VARMAX Procedure

OUTEST= Data Set

The OUTEST= data set contains estimation results of the fitted model produced by the VARMAX statement. The following output variables can be created:

BY variables
NAME, a character variable that contains the name of the endogenous (dependent) variables or the name of the parameters for the covariance of the matrix of the parameter estimates if you specify the OUTCOV option
TYPE, a character variable that contains the value EST for parameter estimates, the value STD for standard error of parameter estimates, and the value COV for the covariance of the matrix of the parameter estimates if you specify the OUTCOV option
CONST, a numeric variable that contains the estimates of constant parameters and their standard errors
SEASON $\_ i$ , a numeric variable that contains the estimates of seasonal dummy parameters and their standard errors, where $i=1,\ldots , (nseason-1)$ , and $nseason$ is based on the NSEASON= option
LTREND, a numeric variable that contains the estimates of linear trend parameters and their standard errors
QTREND, a numeric variable that contains the estimates of quadratic trend parameters and their standard errors
XL $l\_ i$ , numeric variables that contain the estimates of exogenous parameters and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , r$ , where $r$ is the number of exogenous variables
AR $l\_ i$ , numeric variables that contain the estimates of autoregressive parameters and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ , where $k$ is the number of endogenous variables
MA $l\_ i$ , numeric variables that contain the estimates of moving-average parameters and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ , where $k$ is the number of endogenous variables
COV $\_ i$ , numeric variables that contain the estimates of the covariance of innovations parameters when the maximum likelihood method is applied, where $i=1,\ldots , k$
DCCAB, a numeric variable that contains the estimates of $\alpha$ or $\beta$ in the correlation equation for DCC representation and their standard errors
CCC $\_ i$ , numeric variables that contain the estimates of the conditional constant correlation parameters for CCC representation, where $i=2,\ldots , k$
DCCS $\_ i$ , numeric variables that contain the estimates of the unconditional correlation parameters for DCC representation, where $i=2,\ldots , k$
GCHC $\_ i$ , numeric variables that contain the estimates of the constant parameters of the covariance matrix and their standard errors, where $i=1,\ldots , k$ for BEKK representation, $k$ is the number of endogenous variables, and $i=1$ for CCC and DCC representations
ACH $l\_ i$ , numeric variables that contain the estimates of the ARCH parameters of the covariance matrix and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ for BEKK, CCC, and DCC representations, where $k$ is the number of endogenous variables
EACH $l\_ i$ , numeric variables that contain the estimates of the exponential ARCH parameters of the covariance matrix and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ for CCC and DCC representations, where $k$ is the number of endogenous variables
PACH $l\_ i$ , numeric variables that contain the estimates of the power ARCH parameters of the covariance matrix and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ for CCC and DCC representations, where $k$ is the number of endogenous variables
QACH $l\_ i$ , numeric variables that contain the estimates of the quadratic ARCH parameters of the covariance matrix and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ for CCC and DCC representations, where $k$ is the number of endogenous variables
TACH $l\_ i$ , numeric variables that contain the estimates of the threshold ARCH parameters of the covariance matrix and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ for CCC and DCC representations, where $k$ is the number of endogenous variables
GCH $l\_ i$ , numeric variables that contain the estimates of the GARCH parameters of the covariance matrix and their standard errors, where $l$ is the lag $l$ th coefficient matrix and $i=1,\ldots , k$ for BEKK, CCC, and DCC representations, where $k$ is the number of endogenous variables
LAMBDA, a numeric variable that contains the estimates of power parameters in the PGARCH model for CCC and DCC representations and their standard errors

The OUTEST= data set contains the values shown in Table 35.9 for a bivariate case.

Table 35.9: OUTEST= Data Set

Obs	NAME	TYPE	CONST	AR1_1	AR1_2	AR2_1	AR2_2
1	y1	EST	$\delta _1$	$\phi _{1,11}$	$\phi _{1,12}$	$\phi _{2,11}$	$\phi _{2,12}$
2		STD	se( $\delta _1$ )	se( $\phi _{1,11}$ )	se( $\phi _{1,12}$ )	se( $\phi _{2,11}$ )	se( $\phi _{2,12}$ )
3	y2	EST	$\delta _2$	$\phi _{1,21}$	$\phi _{1,22}$	$\phi _{2,21}$	$\phi _{2,22}$
4		STD	se( $\delta _2$ )	se( $\phi _{1,21}$ )	se( $\phi _{1,22}$ )	se( $\phi _{2,21}$ )	se( $\phi _{2,22}$ )

Consider the following example:

proc varmax data=simul2 outest=est;
   model y1 y2 / p=2 noint
                 ecm=(rank=1 normalize=y1)
                 noprint;
run;

proc print data=est;
run;

The output in Figure 35.67 shows the results of the OUTEST= data set.

Figure 35.67: OUTEST= Data Set

Obs	NAME	TYPE	AR1_1	AR1_2	AR2_1	AR2_2
1	y1	EST	-0.46680	0.91295	-0.74332	-0.74621
2		STD	0.04786	0.09359	0.04526	0.04769
3	y2	EST	0.10667	-0.20862	0.40493	-0.57157
4		STD	0.05146	0.10064	0.04867	0.05128