The VARMAX Procedure

OUTHT= Data Set

The OUTHT= data set contains predictions of conditional covariance matrices of innovations of the fitted GARCH model that the GARCH statement produces. The following output variables can be created:

  • the BY variables, if BY-group processing is performed

  • the ID variable, if the ID statement is specified

  • H$i\_ j$, numeric variables that contain the prediction of covariance, where $1 \leq i \leq j \leq k$, where k is the number of dependent variables

The OUTHT= data set contains the values shown in Table 35.10 for a bivariate case.

Table 35.10: OUTHT= Data Set

Obs

H1_1

H1_2

H2_2

1

h111

h121

h221

2

h112

h122

h222

:

:

:

:


The OUTHT= data set has the same number of observations as the OUT= data set. Both the OUTHT= and OUT= data sets include any observations at the beginning of the data set that are skipped because of the DIF=, DIFY=, DIFX=, P=, or XLAG= option and include the predicted observations at the end of the data set, which correspond with the LEAD= specification. If you specify an ID statement together with the OUTHT= and OUT= options, then the values of the ID variable in the two data sets correspond with one another.

Consider the following example of the OUTHT= option:

data garch;
   set garch;
   date = intnx( 'month', '01may1972'd, _n_-1 );
   format date yymms.;
run;

proc varmax data=garch;
   id date interval=month;
   model y1 y2 / p=1;
   garch q=1 outht=ht;
   output out=og lead=6;
run;
proc print data=og(obs=8);
   var date y1 for1 std1 lci1 uci1 y2 for2 std2 lci2 uci2;
run;
proc print data=ht(obs=8);
run;
proc print data=og(firstobs=499);
   var date y1 for1 std1 lci1 uci1 y2 for2 std2 lci2 uci2;
run;
proc print data=ht(firstobs=499);
run;

The output in Figure 35.68 and Figure 35.69 shows the first eight observations in the OUT= and OUTHT= data sets, respectively. The first observation is skipped in the GARCH model estimation because of the P=1 option, resulting in the missing values in the first observations in the OUT= and OUTHT= data sets. The output in Figure 35.70 and Figure 35.71 shows the last eight observations in the OUT= and OUTHT= data sets, respectively. In the OUT= data set, the standard deviations of the forecast of dependent variables are time-variant. The last six observations in OUTHT= data set are the multistep forecast of conditional covariance matrices of innovations.

Figure 35.68: First Part of OUT= Data Set

Obs date y1 FOR1 STD1 LCI1 UCI1 y2 FOR2 STD2 LCI2 UCI2
1 1972/05 -4.4005 . . . . 1.83794 . . . .
2 1972/06 -8.0533 -4.2140 3.10387 -10.2975 1.86947 1.59720 1.92227 1.92885 -1.85820 5.70274
3 1972/07 -10.8362 -8.5587 3.21511 -14.8602 -2.25720 1.51833 -0.37752 1.33100 -2.98623 2.23118
4 1972/08 -6.0179 -11.9245 2.97553 -17.7564 -6.09254 -1.57445 -2.09795 1.75464 -5.53697 1.34108
5 1972/09 -7.8272 -4.3716 3.63437 -11.4949 2.75160 -0.03774 -0.09637 1.44118 -2.92102 2.72829
6 1972/10 -8.4293 -7.4084 3.14734 -13.5770 -1.23969 -0.40424 -0.73442 1.26093 -3.20580 1.73695
7 1972/11 -7.8156 -7.9499 2.89408 -13.6222 -2.27757 0.20642 -1.21238 1.26383 -3.68944 1.26469
8 1972/12 -8.0182 -7.5245 2.87208 -13.1537 -1.89535 0.43513 -0.65343 1.61823 -3.82511 2.51825



Figure 35.69: First Part of OUTHT= Data Set

Obs date h1_1 h1_2 h2_2
1 1972/05 . . .
2 1972/06 9.6340 0.14073 3.72045
3 1972/07 10.3369 0.42643 1.77155
4 1972/08 8.8538 -1.19603 3.07876
5 1972/09 13.2086 1.36328 2.07699
6 1972/10 9.9058 -0.02914 1.58995
7 1972/11 8.3757 -0.29722 1.59728
8 1972/12 8.2489 -0.12736 2.61868



Figure 35.70: Last Part of OUT= Data Set

Obs date y1 FOR1 STD1 LCI1 UCI1 y2 FOR2 STD2 LCI2 UCI2
499 2013/11 -6.1917 -4.1545 2.88303 -9.8051 1.4962 6.09470 6.33899 1.43651 3.5235 9.1545
500 2013/12 -10.2133 -8.6817 2.97211 -14.5070 -2.8565 2.88544 2.11833 1.28490 -0.4000 4.6367
501 2014/01 . -11.8921 2.92171 -17.6186 -6.1657 . -1.30455 1.33400 -3.9191 1.3100
502 2014/02 . -11.7095 4.83388 -21.1837 -2.2353 . -3.59592 2.37237 -8.2457 1.0538
503 2014/03 . -10.2617 6.20050 -22.4145 1.8910 . -4.17796 3.77457 -11.5760 3.2201
504 2014/04 . -8.1778 7.02293 -21.9425 5.5869 . -3.47144 4.98630 -13.2444 6.3015
505 2014/05 . -6.0032 7.41997 -20.5461 8.5396 . -1.98718 5.81618 -13.3867 9.4123
506 2014/06 . -4.1332 7.56318 -18.9567 10.6904 . -0.21231 6.27549 -12.5120 12.0874



Figure 35.71: Last Part of OUTHT= Data Set

Obs date h1_1 h1_2 h2_2
499 2013/11 8.31189 -0.42221 2.06356
500 2013/12 8.83341 -0.00565 1.65098
501 2014/01 8.53639 -0.48367 1.77955
502 2014/02 9.42359 -0.13271 2.47088
503 2014/03 9.55818 -0.00081 2.85906
504 2014/04 9.58107 0.04780 3.07044
505 2014/05 9.58585 0.06690 3.18347
506 2014/06 9.58718 0.07508 3.24331