?GMPROC PROCEDURE HAS BEEN DEFINED BELOW;
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?GENERAL MOMENTS ESTIMATION PROCEDURE FOR ESTIMATION OF RHOH    * 
?MOMENT EQUATIONS INVOLVING                                     * 
?E’E, (ME)’(ME),  AND (ME)’E, WHERE ME=WEIGHTINGMATRIX*E        *
?****************************************************************

SMPL 1 NS;
MMAKE UHVEC UH;
MAT VHVEC = MMAT*UHVEC;
MAT WHVEC = MMAT*VHVEC;
UNMAKE VHVEC VH;
UNMAKE WHVEC WH;

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?CALCULATE VARIOUS SAMPLE MOMENTS APPEARING IN THE SYSTEM       *
?OF EQUATIONS FOR RHO FROM ESTIMATED DISTURBANCES               *
?****************************************************************

GENR U2H  = UH*UH;
GENR V2H  = VH*VH;
GENR UVH  = UH*VH;
GENR VWH  = VH*WH;
GENR W2H  = WH*WH;
GENR UWH  = UH*WH;

MSD (SILENT) U2H V2H UVH VWH W2H UWH ;

SET U2HM  = @MEAN(1); 
SET V2HM  = @MEAN(2);
SET UVHM  = @MEAN(3);
SET VWHM  = @MEAN(4); 
SET W2HM  = @MEAN(5);
SET UWHM  = @MEAN(6);

?CALCULATE TR(MMAT'MMAT)/(SAMPLE SIZE)
?***************************************************************
MAT MMM = TR(MMAT'MMAT)/NS;

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?PREPARE ESTIMATION OF RHO AND S FROM THREE EQUATIONS BY NLS  * 
?****************************************************************

FRML EQU HMY = HM1*RHOGM + HM2*RHOGM**2 + HMS2*SGM;

SMPL 1 3;
GENR HM1  = 0;
GENR HM2  = 0;
GENR HMS2 = 0;
GENR HMY  = 0;

SMPL 1 1;
GENR HM1  = -2*UVHM;
GENR HM2  = V2HM;
GENR HMS2 = -1;
GENR HMY  = -U2HM;

SMPL 2 2;
GENR HM1  = -2*VWHM;
GENR HM2  = W2HM;
GENR HMS2 = -MMM;
GENR HMY  = -V2HM;

SMPL 3 3;
GENR HM1  = -(V2HM+UWHM);
GENR HM2  = VWHM;
GENR HMS2 = 0;
GENR HMY  = -UVHM;

SMPL 1 3;

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SMPL 1 3;
PARAM RHOGM SGM ;
LSQ (SILENT,MAXIT=500,MAXSQZ=20,TOL=0.001) EQU;
TITLE 'STEP 2:  NLS ESTIMATORS OF RHO AND SIGMA^2';
PRINT RHOGM;
PRINT SGM;