Issues with DCC-GARCH

[OS27]

Hello,

I am new to RATS and so far I am finding it pretty nice compared to other software I have used. I have three questions regarding DCC-GARCH and would be more than grateful for any help.

First, when estimating the model on some equity returns, I believe the estimation is getting stuck in a non-concave region. How exactly can I solve this perhaps through altering the initial values but I don't know how to do this? I have scaled my data up and tried different algorithms they don't seem to be helping.

See the error message below:

Code: Select all

GARCH(P=1,Q=1,MV=DCC) / SPRET KSARET

MV-DCC GARCH  - Estimation by BFGS
NO CONVERGENCE IN 7 ITERATIONS. FINAL NORMED GRADIENT    0.04951
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY DIFFERENT SETTING FOR EXACTLINE, DERIVES OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES/PMETHOD OPTION MIGHT ALSO WORK

My second question is more related to the interpretation. That is, if the first DCC coefficient is insignificant and the second is significant does this mean that there is still some evidence for dynamic correlations or should one totally abandon the DCC and go for perhaps the CCC model? Also, would the outputted dynamic correlations still be valid?

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Usable Observations                       366
Log Likelihood                        NA

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Mean(SPRET)                  -0.273364416  0.109934316     -2.48662  0.01289646
2.  Mean(RERET)                 -0.218417507  0.160865868     -1.35776  0.17453932

3.  C(1)                          2.592543476  0.158947483     16.31069  0.00000000
4.  C(2)                          4.716583050  0.189612122     24.87490  0.00000000
5.  A(1)                          0.099861751  0.005810396     17.18674  0.00000000
6.  A(2)                          0.130397286  0.006486436     20.10307  0.00000000
7.  B(1)                          0.433140667  0.018637265     23.24057  0.00000000
8.  B(2)                          0.401311600  0.017801778     22.54334  0.00000000
9.  DCC(A)                       -0.000000000  0.001566448 -2.08750e-09  1.00000000
10. DCC(B)                        0.558063952  0.100507379      5.55247  0.00000003

My final question is simply how to extract the correlation graphs post-estimation?

Your help would be much appreciated!

[TomDoan]

To answer the last question first, the process for getting correlations is the same for any type of multivariate GARCH model. See

https://estima.com/docs/RATS%209%20User ... f#page=328

Since you haven't gotten the model to converge, the second really can't be answered. However, note that B=1, A=0 is actually the same thing as CC---it's the contribution of the DCC(A) that makes the correlations "dynamic". (The B will almost always be very, very "significant").

What kind of data are these? You have fewer than 400 data points and the "GARCH" properties of the series seem fairly weak.

[OS27]

To answer the last question first, the process for getting correlations is the same for any type of multivariate GARCH model. See

https://estima.com/docs/RATS%209%20User ... f#page=328

Since you haven't gotten the model to converge, the second really can't be answered. However, note that B=1, A=0 is actually the same thing as CC---it's the contribution of the DCC(A) that makes the correlations "dynamic". (The B will almost always be very, very "significant").

What kind of data are these? You have fewer than 400 data points and the "GARCH" properties of the series seem fairly weak.

They are weekly closing prices for emerging/frontier equity indices and the S&P 500. I have tried using daily data but am getting the same problem and a paper I have seen uses weekly data for a shorter time period than mine (published in Journal of Banking and Finance).

Do you know any way I could try and get the model to converge? I've used different algorithms and scaled the data up. The only thing I could probably do now is alter the initial values but I have no idea how to...

[TomDoan]

You would have to post your data.

[OS27]

You would have to post your data.

Hello Tom,

Please find the data attached. I am trying to measure the correlations between SP (S&P 500) and the other indices. Your help would be greatly appreciated

[TomDoan]

If you try Middle Eastern countries with each other DCC seems to work OK. The SP500 with KSA are pretty close to being (conditionally) uncorrelated, and those wild downward spikes in the KSA data are going to throw off DCC calculations. CC/DCC are really designed to work with series which have fairly similar dynamics and these don't.

[OS27]

Hmm. Thanks a lot for your help Tom. I was playing around with a DBEKK model to study the volatility spillovers between these markets and found evidence of either uni-directional (SP to Middle East) or no spillovers. I know the models are different and I'd have to alter the framing of the research slightly but do you think the BEKK could be useful in studying the relationship between these markets given their dynamics?

[TomDoan]

It might help, but a BEKK on the SP and KSA barely fits better than a diagonal model (which computes a likelihood assuming zero correlation between the two). The two don't nest, so that isn't a formal test, but 5 extra parameters for a 3.0 gain in the log likelihood isn't very good. It just looks like there is no discernible connection between these two markets. (Which is a result---sometimes zero is the right answer).