Hi,
I was wondering how can someone get the correlation coefficients (ρ) along with their significant values in the DCC model of Engle (2002). Running a simple DCC one gets the results for the mean (constant + exogenous if any) and the variance specification equation (constant + alpha + beta + exogenous if any) but not the coefficients of the correlation estimates along with their significant values.
For instance in another software OxMetrics 5 + G@RACH 5 package when one performs a DCC model of Engle, gets the estimates and the significant values of the correlations coefficients.
However in RATS not.
Could someone help me on this matter on RATS?
Where are the correlation coefficients in the DCC model?
If you look at GARCHMV.PRG, it computes and graphs the correlations from a multivariate GARCH. For any type of multivariate GARCH model, you can get the correlations by saving the series of H matrices and converting to correlations by something like
set rho12 = hh(t)(1,2)/sqrt(hh(t)(1,1)*hh(t)(2,2))
for the correlation between 1 and 2, and similarly for other combinations.
set rho12 = hh(t)(1,2)/sqrt(hh(t)(1,1)*hh(t)(2,2))
for the correlation between 1 and 2, and similarly for other combinations.
Thanks TomDoan for your response.TomDoan wrote:If you look at GARCHMV.PRG, it computes and graphs the correlations from a multivariate GARCH. For any type of multivariate GARCH model, you can get the correlations by saving the series of H matrices and converting to correlations by something like
set rho12 = hh(t)(1,2)/sqrt(hh(t)(1,1)*hh(t)(2,2))
for the correlation between 1 and 2, and similarly for other combinations.
I have already done that. But my question is still whether one gets "parameter estimates of the rho12 (correlation coefficient) along with its standard errors and its significant values.
For instance according to a normal bivariate DCC GARCH output on RATS under the specification given on "GARCHMV.PRG" the output is:
MV_GARCH, DCC - Estimation by BFGS
Convergence in 73 Iterations. Final criterion was 0.0000000 < 0.0000100
Usable Observations 2669
Log Likelihood 7452.40191404
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. C(1) 0.001 0.0005 2.116 0.034
2. C(2) 0.003 0.001 2.21 0.027
3. A(1) 0.035 0.006 5.818 0.000
4. A(2) 0.042 0.007 5.978 0.000
5. B(1) 0.959 0.007 135.921 0.000
6. B(2) 0.951 0.007 121.721 0.000
7. DCC(1) 0.018 0.004 4.505 0.000
8. DCC(2) 0.979 0.004 221.627 0.000
9. Shape 5.829 0.447 13.013 0.000
However, should not be reasonable to have one more parameter estimate for the rho12, so that the out come should look like this:
MV_GARCH, DCC - Estimation by BFGS
Convergence in 73 Iterations. Final criterion was 0.0000000 < 0.0000100
Usable Observations 2669
Log Likelihood 7452.40191404
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. C(1) 0.001 0.0005 2.116 0.034
2. C(2) 0.003 0.001 2.21 0.027
3. A(1) 0.035 0.006 5.818 0.000
4. A(2) 0.042 0.007 5.978 0.000
5. B(1) 0.959 0.007 135.921 0.000
6. B(2) 0.951 0.007 121.721 0.000
7. DCC(1) 0.018 0.004 4.505 0.000
8. DCC(2) 0.979 0.004 221.627 0.000
9. Shape 5.829 0.447 13.013 0.000
10. rho12 0.042 0.007 5.978 0.000
Looking forward to hearing from you.