The VARMAX Procedure

OUTSTAT= Data Set

The OUTSTAT= data set contains estimation results of the fitted model produced by the VARMAX statement. The following output variables can be created. The subindex i is $1,\ldots , k$, where k is the number of endogenous variables.

  • the BY variables

  • NAME, a character variable that contains the name of endogenous (dependent) variables

  • SIGMA$\_ i$, numeric variables that contain the estimate of the innovation covariance matrix

  • AICC, a numeric variable that contains the corrected Akaike’s information criterion value

  • HQC, a numeric variable that contains the Hannan-Quinn’s information criterion value

  • AIC, a numeric variable that contains the Akaike’s information criterion value

  • SBC, a numeric variable that contains the Schwarz Bayesian’s information criterion value

  • FPEC, a numeric variable that contains the final prediction error criterion value

  • FValue, a numeric variable that contains the $F$ statistics

  • PValue, a numeric variable that contains p-value for the $F$ statistics

If the JOHANSEN= option is specified, the following items are added:

  • Eigenvalue, a numeric variable that contains eigenvalues for the cointegration rank test of integrated order 1

  • RestrictedEigenvalue, a numeric variable that contains eigenvalues for the cointegration rank test of integrated order 1 when the NOINT option is not specified

  • Beta$\_ i$, numeric variables that contain long-run effect parameter estimates, $\bbeta $

  • Alpha$\_ i$, numeric variables that contain adjustment parameter estimates, $\balpha $

If the JOHANSEN=(IORDER=2) option is specified, the following items are added:

  • EValueI2$\_ i$, numeric variables that contain eigenvalues for the cointegration rank test of integrated order 2

  • EValueI1, a numeric variable that contains eigenvalues for the cointegration rank test of integrated order 1

  • Eta$\_ i$, numeric variables that contain the parameter estimates in integrated order 2, $\bm {\eta }$

  • Xi$\_ i$, numeric variables that contain the parameter estimates in integrated order 2, $\bxi $

The OUTSTAT= data set contains the values shown Table 35.11 for a bivariate case.

Table 35.11: OUTSTAT= Data Set

Obs

NAME

SIGMA_1

SIGMA_2

AICC

RSquare

FValue

PValue

1

y1

$\sigma _{11}$

$\sigma _{12}$

$aicc$

$R^2_1$

$F_1$

$prob_1$

2

y2

$\sigma _{21}$

$\sigma _{22}$

.

$R^2_2$

$F_2$

$prob_2$


Obs

EValueI2_1

EValueI2_2

EValueI1

Beta_1

Beta_2

1

$e_{11}$

$e_{12}$

$e_{1}$

$\beta _{11}$

$\beta _{12}$

2

$e_{21}$

.

$e_{2}$

$\beta _{21}$

$\beta _{21}$

Obs

Alpha_1

Alpha_2

Eta_1

Eta_2

Xi_1

Xi_2

1

$\alpha _{11}$

$\alpha _{12}$

$\eta _{11}$

$\eta _{12}$

$\xi _{11}$

$\xi _{12}$

2

$\alpha _{21}$

$\alpha _{22}$

$\eta _{21}$

$\eta _{22}$

$\xi _{21}$

$\xi _{22}$

Consider the following example: 

proc varmax data=simul2 outstat=stat;
   model y1 y2 / p=2 noint
                 cointtest=(johansen=(iorder=2))
                 ecm=(rank=1 normalize=y1)
                 noprint;
run;

proc print data=stat;
run;

The output in Figure 35.72 shows the results of the OUTSTAT= data set.

Figure 35.72: OUTSTAT= Data Set

Obs NAME SIGMA_1 SIGMA_2 AICC HQC AIC SBC FPEC RSquare FValue PValue EValueI2_1 EValueI2_2 EValueI1 Beta_1 Beta_2 Alpha_1 Alpha_2 Eta_1 Eta_2 Xi_1 Xi_2
1 y1 94.7557 4.527 9.37221 9.43236 9.36834 9.52661 11712.14 0.93900 482.308 6.1637E-57 0.98486 0.95079 0.50864 1.00000 1.00000 -0.46680 0.007937 -0.012307 0.027030 54.1606 -52.3144
2 y2 4.5268 109.570 . . . . . 0.93912 483.334 5.6124E-57 0.81451 . 0.01108 -1.95575 -1.33622 0.10667 0.033530 0.015555 0.023086 -79.4240 -18.3308