BEKK&DCC

[TomDoan]

It's very strange, but then, again, your data has no GARCH properties, so you can't interpret the coefficients.

[bekkdcc]

Dear Tom,


Before applying BEKK and DCC, I am doing a test that mentioned in

Multivariate GARCH: Basics (Chapter 5) :
We can do a preliminary test for multivariate ARCH effects using the procedure @MVARCHTest. Since this is mainly designed for diagnostics, it assumes that
the input series are already (roughly) mean zero, that is, it doesn’t subtract means itself. We can do the least squares estimates and test for ARCH with

estimate(resids=resids)
@mvarchtest
# resids

and its results just as follow :

Test for Multivariate ARCH
Statistic Degrees Signif
Model-A 316.10 100 0.000 (with 4 variable)
Model-B 168.15 100 0.000 (with 4 variable)
Model-C 1502.91 441 0.000 (with 6 4 variable)


so the result is lack of ARCH is rejected.

Am I right or not? So why do you think there is no GARCH effect? İs there any other test which is more efficient to control it ? or which test I should perform?

Kind regards,

[TomDoan]

You're confusing the null and alternative. What that does is reject homoscedasticity. While it suggests "ARCH" as a possible source, it doesn't mean that any ARCH/GARCH model will actually work. However, it's not a surprise that you would reject homoscedasticity since the inflation data fails an "eyeball test".

The data you have simply will not produce a sensible multivariate GARCH model and particularly will not fit a DCC model, which is designed for a set of relatively similar series, not four series with completely different dynamics. I think I understand what you're trying to do, but as I explained above, it's very unlikely that it will work. The inflation series undergoes a structural change from high and highly variable to low with low variance. Because the levels and the variance move together, there is no way to tell (from the data) which (if either) is responsible for effects on other series. Again, this is in contrast to the oil price in Elder-Serletis which shows many different types of behavior with regard to level and variability.

[TomDoan]

Overall, the impression is that you have a few truly massive outliers. The very low shape coefficient on the t is one sign for that. Also, your second and fourth series have GARCH coefficient patterns (a+b>1) which don't have an unconditional variance, so would be for "spiky" processes. Your mean model doesn't seem to be handling the policy transition properly.

As I've said several times, DCC isn't really the best choice for a set of series which are as different as these---BEKK is the usual choice instead. Whether you have enough data to do a BEKK with four variables is a different matter. However, you need to clean up the basic explanation of the data first before worrying too much about which (if any) GARCH model to use.

[TomDoan]

Dear Tom,

I have 3 problem, and need for your help.

1. I want to draw the ACF of squared residuals of the BEKK model and also standart residuals QQ plot of BEKK model. But I can not do, can you help me how to code it or find it , for the model I use( I give the code That I am using).

set dk = t>=2003:1
set htfe = 1
set x = 1
system(model=mvmean)
variables xtfe xgdp xexcr xfaiz
lags 1
det constant dk htfe x
end(system)
*
garch(model=mvmean,mv=bekk,rvectors=rd,pmethod=simplex,piters=2,method=bfgs,iters=1000, hmatrices=hh,hadjust=%(htfe=sqrt(hh(t)(1,1)), x=dk*htfe))


***For diagnostic Multivariate diagnostics

dec vect[series] rstd(%nvar)
do time=%regstart(),%regend()
eigen(scale) hh(time) * eigfac
compute %pt(rstd,time,%solve(eigfac,rd(time)))
end do time
*
@mvqstat(lags=10,dfc=16)
# rstd
@mvarchtest(lags=2)
# rstd

For squaered residuals ACF and QQ plot? What should I use.

The ACF on the squared residuals is otherwise known as the McLeod-Li test. There's not only a stand-alone procedure for that, but it's also part of the @BDINDTESTS procedure that's used in the GARCHMV.RPF example for univariate diagnostics.

There's a @QPLOT procedure for doing a Q plot against the Normal. However, particularly in the case of a GARCH model, a Q plot really is just a waste of space. Since the GARCH estimates are robust to departures from Normality as a QMLE, it doesn't really matter much if the residuals fail an (eye-ball) test for Normality. A J-B test can be used if you need a test for that anyway.

2. I want to graph the time varying correlations between variables, but which code I should use for my code. I am a bit confused and could not be sure about which notation shoul I use.

There's an example of that as part of the GARCHMV.RPF example and it's described in the User's Guide (Section 9.4.4.).

3. I want to use Engle and Sheppard's (2001) test for presence of dynamic corelation in the residuals of DCC(1,1) ...(The p value and chi-square value) . Should I estimate the model as CCC and then perform the

garch(model=mvmean,mv=cc,rvectors=rd,hmatrices=hh,hadjust=%(htfe=sqrt(hh(t)(1,1)), x=dk*htfe),derives=dd)
@tsecctest(rvector=rd,hmatrices=hh,derives=dd)
@mvjb(factor=%identity(4)) rstd

We do not have the Engle-Sheppard test. We do have the Tse test. I'm not sure whether either one of them can handle a GARCH model with an M effect. If it does extend, then what you did there shows the Tse test. Again, don't confuse null with alternative. The null is that CC is correct, so you might reject CC, but it doesn't mean that DCC is correct. I think I've already pointed out (multiple times) that DCC isn't designed for your type of data.

[bekkdcc]

Dear Tom,

I also want to perform a casuality analysis and also impulse response and variance composition to the BEKK model. Can I do that to my model( which contain MEAN) ? Is there an code-example?

[TomDoan]

For causality, see https://estima.com/forum/viewtopic.php?f=11&t=1274. Impulse responses work the same way after the GARCH as they do for a VAR (use IMPULSE), except you have to choose shocks (typically unit shocks) since there is no fixed covariance matrix. The error decomposition really doesn't make sense in the context of a GARCH model.

[bekkdcc]

Dear Tom,

I want to apply a trivariate DCC model(variables are inflation;output and interest) to 7 country . I use a Var(2) model for each one of the country...

For example ;

First country
inf1=a0+b*inf(1)+c*output(1)+d*int(1)+e
output1=a1+e*inf(1)+f*output(1)+g*int(1)+e
interest1=a2+h*inf(1)+ı*output(1)+k*int(1)+e

Second country
inf2=a3+l*inf(1)+m*output(1)+n*int(1)+e
output2=a4+o*inf(1)+p*output(1)+r*int(1)+e
interest2=a5+s*inf(1)+t*output(1)+v*int(1)+e

and so on....

Of course, I can aplly a dcc model each of the country and get results.

But I am not sure that if ı can modified that as a panel model system, I look for "Mgarch model(especially dcc) in panel data" but could not able to find anything.

[TomDoan]

Nothing that you've said indicates that there is anything "panel" about this. You have two separate GARCH models on two separate data sets.