The VARMAX Procedure

/* Data 'a' Generated Process */
proc iml;
   sig = {1.0  0.5, 0.5  1.25};
   phi = {1.2 -0.5, 0.6  0.3};
   call varmasim(y,phi) sigma = sig n = 100 seed = 46859;
   cn = {'y1' 'y2'};
   create a from y[colname=cn];
   append from y;
run;;

/* when the series has a linear trend */
proc varmax data=a;
   model y1 y2 / p=1 trend=linear;
run;

/* Fit subset of AR order 1 and 3 */
proc varmax data=a;
   model y1 y2 / p=(1,3);
run;

/* Check if the series is nonstationary */
proc varmax data=a;
   model y1 y2 / p=1 dftest print=(roots);
run;

/* Fit VAR(1) in differencing */
proc varmax data=a;
   model y1 y2 / p=1 print=(roots) dify=(1);
run;

/* Fit VAR(1) in seasonal differencing */
proc varmax data=a;
   model y1 y2 / p=1 dify=(4) lagmax=5;
run;

/* Fit VAR(1) in both regular and seasonal differencing */
proc varmax data=a;
   model y1 y2 / p=1 dify=(1,4) lagmax=5;
run;

/* Fit VAR(1) in different differencing */
proc varmax data=a;
   model y1 y2 / p=1 dif=(y1(1,4) y2(1)) lagmax=5;
run;

/* Options related to prediction */
proc varmax data=a;
   model y1 y2 / p=1 lagmax=3
                 print=(impulse covpe(5) decompose(5));
run;

/* Options related to tentative order selection */
proc varmax data=a;
   model y1 y2 / p=1 lagmax=5 minic
                 print=(parcoef pcancorr pcorr);
run;

/* Automatic selection of the AR order */
proc varmax data=a;
   model y1 y2 / minic=(type=aic p=5);
run;

/* Compare results of LS and Yule-Walker Estimators */
proc varmax data=a;
   model y1 y2 / p=1 print=(yw);
run;

/* BVAR(1) of the nonstationary series y1 and y2 */
proc varmax data=a;
   model y1 y2 / p=1
      prior=(lambda=1 theta=0.2 ivar);
run;

/* BVAR(1) of the nonstationary series y1 */
proc varmax data=a;
   model y1 y2 / p=1
      prior=(lambda=0.1 theta=0.15 ivar=(y1));
run;

/* Data 'b' Generated Process */
proc iml;
   sig = { 0.5  0.14 -0.08 -0.03,  0.14 0.71 0.16 0.1,
          -0.08 0.16  0.65  0.23, -0.03 0.1  0.23 0.16};
   sig = sig * 0.0001;
   phi = {1.2 -0.5 0.  0.1,  0.6 0.3 -0.2  0.5,
          0.4  0. -0.2 0.1, -1.0 0.2  0.7 -0.2};
   call varmasim(y,phi) sigma = sig n = 100 seed = 32567;
   cn = {'y1' 'y2' 'y3' 'y4'};
   create b from y[colname=cn];
   append from y;
quit;

/* Cointegration Rank Test using Trace statistics */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 cointtest;
run;

/* Cointegration Rank Test using Max statistics */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 cointtest=(johansen=(type=max));
run;

/* Common Trends Test using Filter(Differencing) statistics */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 cointtest=(sw);
run;

/* Common Trends Test using Filter(Residual) statistics */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 cointtest=(sw=(type=filtres lag=1));
run;

/* Common Trends Test using Kernel statistics */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 cointtest=(sw=(type=kernel lag=1));
run;

/* Cointegration Rank Test for I(2) */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 cointtest=(johansen=(iorder=2));
run;

/* Fit VECM(2) with rank=3 */
proc varmax data=b;
   model y1-y4 / p=2 lagmax=4 print=(roots iarr)
                 ecm=(rank=3 normalize=y1);
run;

/* Weak Exogenous Testing for each variable */
proc varmax data=b outstat=bbb;
   model y1-y4 / p=2 lagmax=4
                 ecm=(rank=3 normalize=y1);
   cointeg rank=3 exogeneity;
run;

/* Hypotheses Testing for long-run and adjustment parameter */
proc varmax data=b outstat=bbb;
   model y1-y4 / p=2 lagmax=4
                 ecm=(rank=3 normalize=y1);
   cointeg rank=3 normalize=y1
      h=(1 0 0, 0 1 0, -1 0 0, 0 0 1)
      j=(1 0 0, 0 1 0, 0 0 1, 0 0 0);
run;

/* ordinary regression model */
proc varmax data=grunfeld;
   model y1 y2 = x1-x3;
run;

/* Ordinary regression model with subset lagged terms */
proc varmax data=grunfeld;
   model y1 y2 = x1 / xlag=(1,3);
run;

/* VARX(1,1) with no current time Exogenous Variables */
proc varmax data=grunfeld;
   model y1 y2 = x1 / p=1 xlag=1 nocurrentx;
run;

/* VARX(1,1) with different Exogenous Variables */
proc varmax data=grunfeld;
   model y1 = x3, y2 = x1 x2 / p=1 xlag=1;
run;

/* VARX(1,2) in difference with current Exogenous Variables */
proc varmax data=grunfeld;
   model y1 y2 = x1 / p=1 xlag=2 difx=(1) dify=(1);
run;