VARX-GARCH-BEKK

[mengqi]

Hi. I have a VAR model with some exogenous variables (VARX model) with GARCH-BEKK.
I would like to shock one of the exogenous variables and see the response on endogenous variables. I followed the codes from MONTEEXOGVAR.RPF. But I have got the following errors:

## MAT2. Matrices with Dimensions 13 x 2 and 37 x 0 Involved in + Operation
The Error Occurred At Location 140, Line 6 of loop/block

After loading the data, here's the code I used:

Code: Select all

log wikibtc / lwikibtc
log wikiltc / lwikiltc
log hashbtc / lhashbtc
log hashltc / lhashltc

dec symm[series] hhs(2,2)
clear(zeros) hhs

System(model=varxmodel)
variables logrbtc logrltc
lags 1
deterministic constant lwikibtc lwikiltc tranbtc tranltc lhashbtc lhashltc hhs(1,1) hhs(1,2) hhs(2,1) hhs(2,2)
end(system)

garch(model=varxmodel,p=1,q=1,mvhseries=hhs,pmethod=simplex,piters=15,iters=400,mv=bekk)

MV-GARCH, BEKK - Estimation by BFGS
Convergence in   300 Iterations. Final criterion was  0.0000088 <=  0.0000100

Daily(7) Data From 2013:07:18 To 2015:10:10
Usable Observations                       815
Log Likelihood                      3007.5462

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
Mean Model(LOGRBTC)
1.  LOGRBTC{1}                       0.003961     0.048540      0.08161  0.93495538
2.  LOGRLTC{1}                      -0.060888     0.025538     -2.38416  0.01711817
3.  Constant                         0.065270     0.005284     12.35184  0.00000000
4.  LWIKIBTC                         0.001221     0.001821      0.67076  0.50237027
5.  LWIKILTC                        -0.010644     0.003716     -2.86416  0.00418120
6.  TRANBTC                          0.000001     0.000000      1.40512  0.15998514
7.  TRANLTC                         -0.000000     0.000000     -1.10392  0.26962783
8.  LHASHBTC                         0.001190     0.001675      0.71080  0.47720843
9.  LHASHLTC                        -0.007418     0.004072     -1.82176  0.06849068
10. HHS(1,1)                         3.601336     2.069988      1.73979  0.08189659
11. HHS(2,1)                        -0.341379     0.586829     -0.58174  0.56074500
12. HHS(2,1)                        -0.299380     0.586828     -0.51017  0.60993493
13. HHS(2,2)                         0.189314     0.155689      1.21598  0.22399277
Mean Model(LOGRLTC)
14. LOGRBTC{1}                       0.234504     0.057586      4.07223  0.00004656
15. LOGRLTC{1}                      -0.221549     0.048116     -4.60452  0.00000413
16. Constant                         0.015848     0.020786      0.76242  0.44580866
17. LWIKIBTC                        -0.000866     0.002529     -0.34260  0.73190054
18. LWIKILTC                        -0.005836     0.004538     -1.28598  0.19845073
19. TRANBTC                          0.000001     0.000001      2.02225  0.04315099
20. TRANLTC                         -0.000000     0.000000     -2.84610  0.00442590
21. LHASHBTC                         0.003720     0.001375      2.70541  0.00682204
22. LHASHLTC                        -0.010459     0.003768     -2.77538  0.00551364
23. HHS(1,1)                         9.827492     3.070184      3.20095  0.00136978
24. HHS(2,1)                        -1.975179     1.167724     -1.69148  0.09074576
25. HHS(2,1)                        -2.030299     1.167699     -1.73872  0.08208455
26. HHS(2,2)                         1.039820     0.413709      2.51341  0.01195709

27. C(1,1)                           0.008452     0.000981      8.61617  0.00000000
28. C(2,1)                           0.005727     0.001599      3.58134  0.00034184
29. C(2,2)                           0.008412     0.001259      6.68213  0.00000000
30. A(1,1)                           0.390640     0.045007      8.67949  0.00000000
31. A(1,2)                          -0.240327     0.084271     -2.85185  0.00434656
32. A(2,1)                          -0.022217     0.027378     -0.81149  0.41708505
33. A(2,2)                           0.615771     0.073408      8.38830  0.00000000
34. B(1,1)                           0.898410     0.020091     44.71687  0.00000000
35. B(1,2)                           0.081461     0.042323      1.92473  0.05426300
36. B(2,1)                           0.020049     0.010875      1.84359  0.06524316
37. B(2,2)                           0.853611     0.031737     26.89648  0.00000000



compute lags=4        
compute nstep=16      
compute ndraws=10000  


equation(empty) rateeq lwikibtc

compute nshocks=1
compute nvar   =%nvar
compute fxx    =%decomp(%xx)
compute fwish  =%decomp(inv(%nobs*%sigma))
compute wishdof=%nobs-%nreg
compute betaols=%modelgetcoeffs(varxmodel)
*
declare vect[rect] %%responses(ndraws)
*
infobox(action=define,progress,lower=1,upper=ndraws) "Monte Carlo Integration"
do draw=1,ndraws
   if %clock(draw,2)==1 {
      compute sigmad  =%ranwisharti(fwish,wishdof)
      compute fsigma  =%decomp(sigmad)
      compute betau   =%ranmvkron(fsigma,fxx)
      compute betadraw=betaols+betau
   }
   else
      compute betadraw=betaols-betau
   compute %modelsetcoeffs(varxmodel,betadraw)
   impulse(noprint,model=varxmodel+rateeq,shocks=%unitv(%nvar+1,%nvar+1),flatten=%%responses(draw),steps=nstep)
   infobox(current=draw)
end do draw
infobox(action=remove)

## MAT2. Matrices with Dimensions 13 x 2 and 37 x 0 Involved in + Operation
The Error Occurred At Location 140, Line 6 of loop/block

@mcgraphirf(model=varxmodel,footer="Response to lwikibtc Shock",shocklabels=||"Rate Shock"||)


Could you tell me how to fix the problem in order to get the impulse response from exogenous variable shock?

Thanks

[TomDoan]

Unfortunately, there is no simple way to do inference on a multivariate VARX-GARCH model the way there is with a VARX. With the VARX, the posterior distribution takes a well-known and easily simulated form. The "GARCH" (any type, not just BEKK) is the problem; it does not have a convenient form. Instead, you have to use some form of Markov Chain Monte Carlo. The closest example we have is Elder-Serletis(2010). The good news is that your impulse response functions are quite a bit simpler as, although you also have "M" effects, you're doing shocks to exogenous variables and thus you don't get feedback to the level through the variances.