GARCHGIRF.RPF

GARCHGIRF.RPF is an example of the calculation of a Variance GIRF (Generalized Impulse Response Function) for a multivariate GARCH model. A more detailed example is provided in the Hafner and Herwartz(2006) replication. Note that this is much more complicated than impulse responses for the mean of a process since a variance is naturally non-zero so what constitutes a "shock" is not as clear. (Hafner and Herwartz look at responses to historical episodes). Also, not all typical multivariate GARCH models even admit a Variance GIRF—a DVECH, for instance, has a highly uninteresting Variance GIRF since each component has a separate recursion.

This does the calculations in VECH form.

Full Program

open data g10xrate.xls

data(format=xls,org=columns) 1 6237 usxjpn usxfra usxsui

set xjpn = 100.0*log(usxjpn/usxjpn{1})

set xfra = 100.0*log(usxfra/usxfra{1})

set xsui = 100.0*log(usxsui/usxsui{1})

garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=10,vechmats=vechcomps) / xjpn xfra xsui

compute vcs=vechcomps("C")

compute vas=vechcomps("A")

compute vbs=vechcomps("B")

compute n=%nvar

* Solve for the steady-state covariance matrix.

compute h0vech=%solve(%identity(%rows(vas))-vas-vbs,vcs)

compute h0=%vectosymm(h0vech,n)

compute nstep=20

dec rect[series] girfs(n,n)

do j=1,n

do i=1,n

set girfs(i,j) 1 nstep = 0.0

end do j

* Compute the mean of eps given H0 covariance matrix and shock to

* variable j (defined as have a value double the steady-state

* standard deviation) and take its outer product.

compute vechirf=h0(j,j)*%vech(%outerxx(%unitv(n,j)))

do step=1,nstep

if step==1

compute vechirf=vas*vechirf

else

compute vechirf=(vas+vbs)*vechirf

compute varirf=%vectosymm(vechirf,n)

do i=1,n

compute girfs(i,j)(step)=varirf(i,i)

end do i

end do step

end do j

spgraph(vfields=n,hfields=n,header="Variance Responses in GARCH Model",$

xlabels=||"Japan","France","Switzerland"||,ylabels=||"Japan","France","Switzerland"||)

dec vect[series] resp(n)

do i=1,n

compute minlower=maxupper=0.0

do j=1,n

set resp(j) 1 nstep = girfs(i,j)

end do j

table(noprint) 1 nstep resp

compute maxupper=%max(0.0,%maximum)

compute minlower=%min(0.0,%minimum)

do j=1,n

graph(row=i,col=j,max=maxupper,min=minlower)

# girfs(i,j)

end do j

end do i

spgraph(done)

Output

MV-GARCH, BEKK - Estimation by BFGS

Convergence in 86 Iterations. Final criterion was 0.0000086 <= 0.0000100

Usable Observations 6236

Log Likelihood -11821.7457

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Mean(XJPN) 0.005284238 0.005779110 0.91437 0.36052308

2. Mean(XFRA) -0.002360430 0.004150748 -0.56868 0.56957616

3. Mean(XSUI) -0.002505826 0.004919824 -0.50933 0.61051925

4. C(1,1) 0.082827551 0.005082889 16.29537 0.00000000

5. C(2,1) 0.029966933 0.006774462 4.42352 0.00000971

6. C(2,2) 0.055802023 0.004748283 11.75204 0.00000000

7. C(3,1) 0.037995437 0.007654196 4.96400 0.00000069

8. C(3,2) -0.004017902 0.006806450 -0.59031 0.55498413

9. C(3,3) 0.058506480 0.006245748 9.36741 0.00000000

10. A(1,1) 0.359535262 0.012077169 29.76983 0.00000000

11. A(1,2) 0.102691494 0.009048917 11.34848 0.00000000

12. A(1,3) 0.111082248 0.011812194 9.40403 0.00000000

13. A(2,1) 0.038123247 0.014041254 2.71509 0.00662580

14. A(2,2) 0.403444341 0.016261862 24.80923 0.00000000

15. A(2,3) -0.066355330 0.013370391 -4.96286 0.00000069

16. A(3,1) -0.047522551 0.010449514 -4.54782 0.00000542

17. A(3,2) -0.125553482 0.012149506 -10.33404 0.00000000

18. A(3,3) 0.291344292 0.010526939 27.67607 0.00000000

19. B(1,1) 0.935272064 0.003791535 246.67373 0.00000000

20. B(1,2) -0.026717483 0.003105677 -8.60279 0.00000000

21. B(1,3) -0.028574502 0.004086792 -6.99192 0.00000000

22. B(2,1) -0.012475081 0.005562790 -2.24259 0.02492300

23. B(2,2) 0.909746081 0.006295125 144.51597 0.00000000

24. B(2,3) 0.029269416 0.005403727 5.41652 0.00000006

25. B(3,1) 0.016548608 0.004489013 3.68647 0.00022739

26. B(3,2) 0.048830173 0.004991829 9.78202 0.00000000

27. B(3,3) 0.946852761 0.004722801 200.48544 0.00000000

Graph