simulate multiple forecast paths using proc varmax

[eemrun]

i am trying to simulate multiple scenarios from a VAR model using proc varmax. The idea is that proc varmax provides a forecast series and then multiple scenarios are generated around that series. I am currently running the following model:

ods graphics on;
proc varmax data=in(firstobs = 2) covout Outest = estin Outstat = s  plot = (residual model forecast);
   id ReportingDate interval=quarter align = end ;
   model cpi ump gdp hpi / 
   				 nseason = 4
/*				 cointtest=(johansen)*/
				 Dif = (cpi(1) ump(1) gdp(1) hpi(1)) 
				 p=4
				 	
   				 dftest
				 
                 print=(estimates diagnose);
			     output out=in_fct lead=12;
run;

This gives me a 12 period forecast.

I wanted to know if it is possible using Proc Varmax to generate multiple paths? My understanding is that you can create paths by generating a normally distributed residual distribution and then adding it back to the model estimates. But I am unclear as to how that works out in the procedure or how we can do this in SAS altogether.

[Rick_SAS]

Yes, this is covered in Chapter 11 (pp. 204-207) of Simulating Data with SAS. (Code available from the web site.) Briefly, you estimate the parameters for the model, including the magnitude of the error terms.

The example in the book uses a simple one-variable regression with independent normal errrors. An OLS regression for the Sashelp.Class data is Weight = -143 + 3.9*Height + eps, where eps ~ N(0, 11.23). The following simulation is from p. 205. It simulates 100 data sets, each with different observed errors.

/* duplicate data by using sequential access followed by a sort     */
%let NumSamples = 100;              /* number of samples            */
data StudentSim(drop= b0 b1 rmse);
b0 = -143; b1 = 3.9; rmse = 11.23;  /* parameter estimates          */
call streaminit(1);
set Sashelp.Class;                  /* implicit loop over obs       */
i = _N_;
eta = b0 + b1*Height;               /* linear predictor for student */
do SampleID = 1 to &NumSamples;
   Weight = eta + rand("Normal", 0, rmse);
   output;
end;
run;

proc sort data=StudentSim;
   by SampleID i;
run;

You can then use BY-group analysis to get 100 "new" simulated analyses, each with its own predictions. The book does not have a VARMAX example, but hopefully you can generalize the main ideas of this example.

[eemrun]

This is very useful. Thanks Rick. I will try it out with Varmax