Simulated Method of Moments -- AR(1) Process
/*--------------------------------------------------------------
SAS Sample Library
Name: modex16.sas
Description: Example program from SAS/ETS User's Guide,
The MODEL Procedure
Title: Simulated Method of Moments -- AR(1) Process
Product: SAS/ETS Software
Keys: nonlinear simultaneous equation models
PROC: MODEL
Notes:
--------------------------------------------------------------*/
%let nobs=500;
data ardata;
lu =0;
do i=-10 to &nobs;
x = rannor( 1011 );
e = rannor( 1011 );
u = .6 * lu + 1.5 * e;
Y = 2 + 1.5 * x + u;
lu = u;
if i > 0 then output;
end;
run;
title1 'Simulated Method of Moments for AR(1) Process';
proc model data=ardata ;
parms a b s 1 alpha .5;
instrument x;
u = alpha * zlag(u) + s * rannor( 8003 );
ysim = a + b * x + u;
y = ysim;
moment y = (2) lag1(1);
fit y / gmm npreobs=10 ndraw=10;
bound s > 0, 1 > alpha > 0;
run;