Negative GARCH coefficient in a DCC-GARCH(1,1) model

[vmadhavan]

Hi Tom

I am trying to run a DCC-GARCH model involving 5 time series. One of the five univariate GARCH models that constitute the preliminary step of DCC-GARCH estimation procedure yield a non-negative insignificant GARCH coefficient. The coefficient of all ARCH terms (total terms 5) and the rest of GARCH coefficents (remaining 4) are all positive and significant at 1% level.

The DCC(2) term is insignificant.

How do I impose non-negative constraints in a DCC-GARCH model. Does the insignificant DCC(2) term mean that a DCC route is not the ideal route for analyzing correlations of the different time series considered?

I have enclosed the data,code, and the output files.

Would greatly appreciate if you can help in this regard

Vinodh Madhavan

[TomDoan]

A DCC model really should only be applied to a set of series which are relatively similar since the (in this case 10) cross correlations are all governed by just two parameters. I don't know about the first four series (which show varying degrees of "GARCHness"), but the last is basically white noise with no GARCH effect at all.

BTW, though it will have no effect on the estimation, it would be a good idea to replace all your log(x) by 100*log(x) to get the magnitudes of the mean and C coefficients up closer to 1.

[vmadhavan]

Thanks a lot Tom, I now removed the last time series and then ran a DCC-GARCH(1,1) with 4 time series. No negative ARCH or GARCH coefficients. Sum of all ARCH and GARCH coefficients for each of the 4 time series is less than one.

Instead of GARCH model I tried to model the 5th time series separately using a basic AR(1) model and then tested for ARCH effects using LM test. No ARCH effects are found. I guess this explains the negative insignificant GARCH coefficient for this fifth time series when I run a DCCGARCH model with all 5 time series.

Once again, Thanks a lot Tom.

I just have a question. Would greatly appreciate if you can enlighten me in this regard.

Having used RATS 8.0 to generate some DCC-GARCH models, I have come across scenarios wherein a) all ARCH, GARCH and DCC coefficients are positive(As expected), b) sum of all ARCH and GARCH coefficients less than 1 (As expected), c) DCC(1) coefficient is positive and significant, while DCC(2) coefficient is positive and insignificant

What is the theoretical takeaway from such scenarios? From what I understand, if both DCC(1) and DCC(2) coefficients are insignificant, this breaks down the need for DCC-GARCH model in the first place. Please correct me if I am wrong.

Hoping to hear from you

Vinodh Madhavan

[TomDoan]

If DCC(2) is very close to 1, then the process is closer to being a CC. The "dynamic" part comes from DCC(1). However, in practice, a "large" value for DCC(1) is something like .1 to .2, with DCC(2) being relative close to 1-DCC(1). If both DCC(1) and DCC(2) are fairly small, it means that there appears to be no systematic correlation among the variables.