VAR(1)-BEKK-GARCH(1,1) Model

[humyra]

I am estimating a bivariate VAR(1)-BEKK-GARCH(1,1) model between two financial series to test volatility spillovers and persistence of spillovers from one series to another. I have daily data for 12 years (3220 observations). I want to use the BHHH algorithm to estimate the model.

I wanted to know the exact code to run the above model.

Thanks,
Humyra

[TomDoan]

system(model=varmodel)
variables y1 y2
lags 1 to number_of_lags_you_want
det constant
end(system)
*
garch(model=varmodel,mv=bekk,method=bhhh)

Note, however, that we don't recommend using BHHH as the primary estimation method. See the User's Guide.

[humyra]

I also want to know the code to estimate the variance covariance matrix for my bivariate case, and how to generate the two conditional variance as well as the conditional covariance equations.

Thank you.

[TomDoan]

I also want to know the code to estimate the variance covariance matrix for my bivariate case, and how to generate the two conditional variance as well as the conditional covariance equations.

Thank you.

You don't need "equations". The covariances are generated by the GARCH instruction and can be saved using the HMATRICES or MVHSERIES option depending upon what you want to do.

[humyra]

Is this final code correct if I am estimating a bivariate VAR(1)-BEKK-GARCH(1,1) model? Am I missing out on anything?

system(model=varmodel)
variables y1 y2
lags 1
det constant
end(system)
*
garch(p=1,q=1,model=varmodel,mv=bekk,pmethod=simplex,piters=10,rseries=rs,mvhseries=hhs,stdresids=zu)
*
@mvqstat(lags=5)
# zu
@mvarchtest(lags=5)
# zu

I also tried using the BHHH algorithm but my model did not converge. Any idea why this happened?

[TomDoan]

It depends upon what "doesn't converge" means. If it didn't converge in the standard number of iterations without any nasty looking messages, then just increase the ITERATIONS option. If it gives you a message that the estimation stalled, then it's possible that you're trying to fit a GARCH model to a data set that isn't well explained by a GARCH model. If you can post the output that you're getting, I can probably help you more.

[humyra]

This is the code:

OPEN DATA "C:\Users\Humyra1\Desktop\Humyra - Data.xlsx"
CALENDAR(D) 2005:1:3
DATA(FORMAT=XLSX,ORG=COLUMNS) 2005:01:03 2017:05:05 Citi MXWO

system(model=varmodel)
variables Citi MXWO
lags 1
det constant
end(system)
*
garch(model=varmodel,mv=bekk,method=bhhh,iterations=1000)

However, simplex works fine but I am still getting significant ARCH effects when I apply the mvgarch test.

[TomDoan]

I'm not sure what you did with the data before the GARCH instruction, but this works fine and produces reasonable looking output. Note that it does not converge with BHHH, which is a common problem and why we don't recommend it. (The options for saving the output have no effect on the estimation).


OPEN DATA "C:\TEMP\Humyra - Data.xlsx"
DATA(FORMAT=XLSX,ORG=COLUMNS) 1 3220 Citi MXWO
*
system(model=varmodel)
variables citi mxwo
lags 1
det constant
end(system)
garch(model=varmodel,mv=bekk,pmethod=simplex,piters=10,method=bfgs)

[humyra]

Thank you for all your help!

So I should stick to simplex rather than BHHH.


Wpuld you able to suggest why the mvarchtest on the standard residuals is significant?

Also, I can't seem to display the covariance variance matrix. What's the code for that?

[humyra]

I also want to calculate the the two conditional variance and one conditional covariance equation (I've attached a picture). Is RATS able to do that?

[TomDoan]

Thank you for all your help!

So I should stick to simplex rather than BHHH.


Wpuld you able to suggest why the mvarchtest on the standard residuals is significant?

Also, I can't seem to display the covariance variance matrix. What's the code for that?

First of all, the main estimation algorithm is BFGS, not simplex. Simplex is used for preliminary iterations. You really need to read through the chapter in the User's Guide.

There isn't a covariance matrix---there are 3000 of them, one for each data point. That's why they're generally graphed.

If you realize that a GARCH model isn't intended as a description of the actual process, but only as an approximation, the fact that you don't get an overwhelming rejection with 3000 data points is a good sign.

[TomDoan]

I also want to calculate the the two conditional variance and one conditional covariance equation (I've attached a picture). Is RATS able to do that?

That's just what you get when you multiply out the equations for the BEKK GARCH. That's what the GARCH instruction produces as I described earlier.

[humyra]

Thank you for all your helpful comments. I have read through the user guide but still tend to get confused.

One last thing. When I apply the @mvqtest and @mvarch test with lag 5, this is the output I get:

Multivariate Q(5)= 29.79475
Significance Level as Chi-Squared(20)= 0.07325

Test for Multivariate ARCH
Statistic Degrees Signif
78.32 45 0.00153

However, I have seen a couple of papers with a high number of lags. If I increase lag length to maybe 40, this is what I get:

Multivariate Q(40)= 182.65145
Significance Level as Chi-Squared(160)= 0.10604

Test for Multivariate ARCH
Statistic Degrees Signif
373.69 360 0.29856

What do you think?

Humyra

[TomDoan]

Using a high number of lags seems like a way to get an insignificant result---there's no reason to believe that there will be any residual GARCH effect at lags of 20, 30, 40.

[humyra]

Hi Tom,

I have several questions.

Is there are a way to obtain the three variance equations that I have posted earlier through RATS?

Also, I have seen people posting this command for multivariate diagnostics:

dec vect[series] zu(%nvar)
do time=%regstart(),%regend()
compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
end do time

What does this do?

How are the hmatrices or the rvectors graphed?

Also how can I export all my results to Word or Excel?

Thanks,
Humyra