The code below simulates 25 GARCH(1,1) processes with 1,000 observations each and estimates their out-of-sample conditional variances based on GARCH(p,q) with p,q∈{1,2,3} using an expanding window starting from 100 observations.
resetline;
option nodate nonumber ls=128 ps=max;
proc datasets lib=work kill nolist;
run;
data _01;
format I T SIGMA2 U SIGMA21 U1;
call streaminit(1);
do I=1 to 25;
do T=1 to 1000;
if T=1 then do;
SIGMA21=.;
U1=.;
SIGMA2=1;
end;
else SIGMA2=0.1+0.2*U1**2+0.7*SIGMA21;
U=sqrt(SIGMA2)*rand("normal");
output;
SIGMA21=SIGMA2;
U1=U;
end;
end;
run;
%macro REPEAT1;
%do REPEAT=101 %to 1000;
data _99;
T=&REPEAT.;
set _01(rename=(T=T0) where=(T0<=&REPEAT.));
if T0=&REPEAT. then U=.;
run;
proc append base=_98 data=_99;
run;
%end;
%mend;
%REPEAT1;
ods select none;
ods noresults;
proc autoreg;
by T I;
ods output ConvergenceStatus=_96 FitSummary=_97;
model U=/noint garch=(p=1,q=1) maxiter=10000 converge=0.0001;
output out=_95 ht=GARCH11;
model U=/noint garch=(p=1,q=2) maxiter=10000 converge=0.0001;
output out=_94 ht=GARCH12;
model U=/noint garch=(p=1,q=3) maxiter=10000 converge=0.0001;
output out=_93 ht=GARCH13;
model U=/noint garch=(p=2,q=1) maxiter=10000 converge=0.0001;
output out=_92 ht=GARCH21;
model U=/noint garch=(p=2,q=2) maxiter=10000 converge=0.0001;
output out=_91 ht=GARCH22;
model U=/noint garch=(p=2,q=3) maxiter=10000 converge=0.0001;
output out=_90 ht=GARCH23;
model U=/noint garch=(p=3,q=1) maxiter=10000 converge=0.0001;
output out=_89 ht=GARCH31;
model U=/noint garch=(p=3,q=2) maxiter=10000 converge=0.0001;
output out=_88 ht=GARCH32;
model U=/noint garch=(p=3,q=3) maxiter=10000 converge=0.0001;
output out=_87 ht=GARCH33;
run;
ods results;
ods select all;
data _97(keep=T I Model AIC);
set _97(rename=(nValue2=AIC));
where Label2="AIC";
by T I Model;
if last.Model;
run;
proc transpose out=_97(drop=_NAME_) prefix=AIC;
var AIC;
by T I;
run;
proc transpose data=_96 out=_96(drop=_NAME_) prefix=CONV;
var Status;
by T I;
run;
%macro REPEAT2;
%do REPEAT=95 %to 87 %by -1;
proc sort data=_&REPEAT. out=_&REPEAT. nodupkey;
by T I T0;
run;
%end;
%mend;
%REPEAT2;
data _86;
merge _98(where=(T=T0)) _97 _96
_95(where=(T=T0) keep=T I T0 GARCH11)
_94(where=(T=T0) keep=T I T0 GARCH12)
_93(where=(T=T0) keep=T I T0 GARCH13)
_92(where=(T=T0) keep=T I T0 GARCH21)
_91(where=(T=T0) keep=T I T0 GARCH22)
_90(where=(T=T0) keep=T I T0 GARCH23)
_89(where=(T=T0) keep=T I T0 GARCH31)
_88(where=(T=T0) keep=T I T0 GARCH32)
_87(where=(T=T0) keep=T I T0 GARCH33);
by T I;
array AIC(*) AIC1-AIC9;
array CONV(*) CONV1-CONV9;
array GARCHPQ(*) GARCH11--GARCH33;
do J=1 to 9;
if CONV(J)=3 or GARCHPQ(J)=. then AIC(J)=.;
end;
do J=1 to 9;
if AIC(J)=max(of AIC1-AIC9) then GARCH=GARCHPQ(J);
end;
drop T0 J;
run;
quit;
I don't think there exists a logical problem in the code, but AUTOREG aborts at some point generating two warning messages "ERROR: Floating Point Overflow." and "ERROR: Termination due to Floating Point Exception," respectively. Recursive SAS Macro may be one easy solution, but I want to circumvent the way since it's too costly compared to the code above.
