i have difficuty in programing trivariate VAR(2) GARCH in Mean using FANPACMT. Any suggestion for making option on puting each conditional standard deviation in each mean equations ?

## 1 Answer

The option for a diagonal in-mean for multivariate models is a great suggestion which will get passed on to the developers. In the meantime, you could get the same result by constraining the off-diagonal elements to zero. First, run the model setting `maxIters` to 1 and print the vector of parameters. This will give you the order of the parameters so that you can then use apply linear constraints in `sqpSolvemt`:

library fanpacmt; #include fanpacmt.sdf load index[368,9] = index.asc; x0 = index[.,2:3]; x = 200 * ln(x0[2:368,.]./x0[1:367,.]); struct FanControl f0; f0 = fanControlCreate; f0.p = 1; f0.q = 1; f0.inmean = 1; // nonzero is in-mean model f0.sqrtcv = 1; // square root of conditional variance is used f0.SQPsolveMTControlProc = &sqpc; proc sqpc(struct sqpsolvemtControl c0); c0.maxiters = 1; retp(c0); endp; struct DS d0; d0 = dsCreate; d0.dataMatrix = x; struct fanEstimation out; out = CCCGarch(f0,d0); lbl = pvGetParNames(out.par); x = pvGetParVector(out.par); format /rd 10,4; for i(1,rows(x),1); print lbl[i];; print x[i]; endfor;

beta0[1,1] 0.2759 beta0[2,1] 0.0355 delta_s[1,1] -0.0507 delta_s[1,2] 0.0508 delta_s[2,1] 0.0053 delta_s[2,2] -0.0507 omega[1,1] 2.3277 omega[2,1] 0.6059 garch[1,1] 0.0106 garch[1,2] 0.0201 arch[1,1] 0.1112 arch[1,2] -0.0900 cor[2,1] 0.0509

We will want to constrain the off-diagonal elements of `delta_s` to zero, which are the 4th and 5th parameters of the 13 parameters in the parameter vector. We do this by adding lines to the linear constraints in `sqpSolvemt`:

proc sqpc(struct sqpsolvemtControl c0); c0.printIters = 1; c0.maxiters = 5; local A,B; A = zeros(2,13); B = zeros(2,1); A[1,4] = 1; A[2,5] = 1; c0.A = c0.A | A; c0.B = c0.B | B; retp(c0); endp;

The rows of `A` are the constraints we want to add, and the columns is equal to the number of parameters in the parameter vector. The constraint is *Ax = B* where *x* is the parameter vector. Next rerun the command file and we get

beta0[1,1] 0.3029 beta0[2,1] 0.1124 delta_s[1,1] -0.0223 delta_s[1,2] 0.0000 delta_s[2,1] 0.0000 delta_s[2,2] -0.0220 omega[1,1] 2.3488 omega[2,1] 0.6270 garch[1,1] 0.1316 garch[1,2] 0.0311 arch[1,1] 0.1318 arch[1,2] 0.0311 cor[2,1] 0.1213