VAR-GARCH-M

[TomDoan]

What you have is correct. I had tried some different sample ranges to see if anything changed noticeably. The more strongly positive coefficient is associated with the earlier part of your sample.

[economics2012]

So, could it be that the mean is not correctly specified or that I still have GARCH effects. How can I check for that using RATS?

[TomDoan]

You should do the standard diagnostics on this, but I doubt that minor tweaks to the model will change the result. It's likely that the GARCH variance is a poor proxy for oil price uncertainty in your model. The GARCH variance at t is a function of the data through t-1 so may be missing information. There also might be some timing issues between the two markets.

[economics2012]

Can you please help me in writting the procedure for a bivariate ARCH test? I need to get the LM test and check whether I have ARCH effects in the series.

I tried to follow the below procedure but I got too many errors:



I highly appreciate your help,

[TomDoan]

You just do

@MVARCHTEST
# series1 series2

for whatever the two series are. You don't have to change the procedure.

[economics2012]

Ok, I got the following:
Test for Multivariate ARCH
Statistic Degrees Signif
216.87 9 0.00000

This means that we can reject the null hypothesis of no ARCH errors, correct?

If this is the case ( the existence of a GARCH EFFECT), do you think I should you a different GARCH model? instead of GARCH-IN-MEAN?

Thanks a lot

[TomDoan]

That does show a GARCH effect, but what series are you testing?

[economics2012]

I am testing for the daily aggregate stock returns and oil prices. I haven't tested yet for ARCH effect at the sectoral level!
The series for aggregate stock returns and oil prices is attached below. I also attached the procedure along with the results.

[TomDoan]

You're testing the original data. That is wrong on several levels. It shouldn't come as a surprise that your original data fail a GARCH test, since you've already shown that a VAR-GARCH model fit to it has very significant GARCH coefficients. In addition, you should only apply a GARCH test to a series which is roughly white noise, and you also have serial correlation in the original data. Instead, you want to test standardized residuals from the GARCH estimation. In your case, that would be done with something like:

Code: Select all

dec vect[series] ustd(%nvar)
clear(zeros) ustd
dec series[vect] garchu
compute %%garchinit()
gset garchu gstart gend = bb*yvec(t)-%%garchmu(t)
do time=gstart,gend
   compute %pt(ustd,time,%solve(%decomp(hh(time)),garchu(time)))
end do time
@mvarchtest
# ustd

[economics2012]

Thanks a lot Tom.

I ran the test with the original procedure and this is what I got:

Test for Multivariate ARCH
Statistic Degrees Signif
17.30 9 0.04424

That does show a GARCH effect, right? So, what do you suggest in this case, should I try different GARCH model such as EGARCH or so? Also, should I run the test for multivariate ARCH on all the sectors I have?

I have attached the procedure along with the results.

Thanks a lot for all your help, I truly appreciate it.

[TomDoan]

Thanks a lot Tom.

I ran the test with the original procedure and this is what I got:

Test for Multivariate ARCH
Statistic Degrees Signif
17.30 9 0.04424

That does show a GARCH effect, right? So, what do you suggest in this case, should I try different GARCH model such as EGARCH or so? Also, should I run the test for multivariate ARCH on all the sectors I have?

I have attached the procedure along with the results.

Thanks a lot for all your help, I truly appreciate it.

A .04 significance level on a GARCH test of the standardized residuals with that much data is a very good result. It's highly unlikely that anything you could do with the GARCH part of the model will give you a better fit. You could try an EGARCH variation or try using conditionally t rather than Normal. I wouldn't expect either to change things all that much.

[economics2012]

SO, what do you think the main reason behind getting this positive effect of oil price uncertainty on stock returns?

[TomDoan]

SO, what do you think the main reason behind getting this positive effect of oil price uncertainty on stock returns?

I mentioned before that the GARCH variance might be a poor proxy for the uncertainty, or there might be timing issues at the daily level. At any rate, interpretation isn't the job of the software, it's the job of the economist.

[economics2012]

Thanks a lot Tom for all your helpful comments.

I still have one question here:

When I ran the bivatiate ARCH test over the sectors as shown below, some show significance and some do not. In such cases, can I say that for instance the auto returns with a sig. of 0.36 does not give me a good fit, while the coal returns with a sig. of 0.000 does give me a good fit?

Again, thanks a lot for your help,

[TomDoan]

You have that backwards. Significance levels near 0 mean that your GARCH model hasn't eliminated all GARCH effects.