Diagnostic test and mean model for BEKK-GARCH
Posted: Sat Aug 04, 2018 5:45 pm
Dear Tom,
I have just estimated a BEKK-GARCH model with the mean model VAR(1) and did diagnostic test to see whether the model is adequate. I did both "univariate" diagnostic and multivariate diagnostic follow the RATS' User Guide.
Here is my diagnostic result:
As you can see the univariate Q test and the univariate McLeod-Li test is insignificant which shows that the univariate standardized residuals are serially uncorrelated. In the mutivariate diagnostics, the multivariate Q is insignificant while the mvarchtest reject strongly. This result is like the example in @GARCHMV.RPF, the results of McLeod-Li test and the mvarchtest are conflicted. But there is no further explaination about that. What is the different between these two tests?
Looking at the RATS' User Guide and your reply in other topics, you said the model is adequate when the MVQSTAT and MVARCHTEST are insignificant. According to that, is it my estimated model above is invalid? Or can I say my model is adequate because of the univariate diagnostics test results? If not, how can I improve my model to be adequate? I have tried to add lags to the VAR mean model, but it is still strongly rejected in MVQSTAT.
Another question: How to decide the mean model before estimating the BEKK model? From the VARMAGARCH.RPF, it says the GARCH with a VAR mean model is common and better than VARMA. In general, it is best to start with a small model and add lags until the model is adequate. So can I use VAR(1) mean model straight away at the beginning? And once the BEKK-GARCH is adequate, there is no problem of using the VAR(1) mean model. In other words, can I say if the estimated BEKK-GARCH model is adequate, which kind of mean model is not of interest?
Thanks,
Haoting
I have just estimated a BEKK-GARCH model with the mean model VAR(1) and did diagnostic test to see whether the model is adequate. I did both "univariate" diagnostic and multivariate diagnostic follow the RATS' User Guide.
Here is my diagnostic result:
Code: Select all
MV-GARCH, BEKK - Estimation by BFGS
Convergence in 60 Iterations. Final criterion was 0.0000041 <= 0.0000100
Weekly Data From 1997:07:08 To 2007:06:26
Usable Observations 521
Log Likelihood -2394.7671
Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(RHK)
1. RHK{1} -0.050488729 0.046670912 -1.08180 0.27934011
2. RUK{1} 0.075863528 0.059254207 1.28031 0.20043747
3. Constant 0.274979114 0.121417868 2.26473 0.02352904
Mean Model(RUK)
4. RHK{1} -0.026833057 0.030589271 -0.87720 0.38037539
5. RUK{1} -0.082991813 0.052566271 -1.57880 0.11438113
6. Constant 0.234809002 0.079567031 2.95108 0.00316661
7. C(1,1) -0.297073107 0.084551821 -3.51350 0.00044224
8. C(2,1) -0.010294091 0.085941519 -0.11978 0.90465728
9. C(2,2) -0.263180811 0.083489962 -3.15224 0.00162020
10. A(1,1) 0.277588736 0.040689037 6.82220 0.00000000
11. A(1,2) 0.065113722 0.022653730 2.87430 0.00404918
12. A(2,1) -0.126032635 0.042071421 -2.99568 0.00273831
13. A(2,2) -0.274239692 0.046336814 -5.91840 0.00000000
14. B(1,1) 0.960850548 0.013777814 69.73897 0.00000000
15. B(1,2) 0.021612663 0.008070182 2.67809 0.00740436
16. B(2,1) 0.012756593 0.016342192 0.78059 0.43504218
17. B(2,2) 0.946374383 0.016052239 58.95591 0.00000000
Independence Tests for Series Z1
Test Statistic P-Value
Ljung-Box Q(40) 33.557567 0.7541
McLeod-Li(40) 41.838360 0.3910
Turning Points 1.769490 0.0768
Difference Sign -1.971055 0.0487
Rank Test 1.508427 0.1314
Independence Tests for Series Z2
Test Statistic P-Value
Ljung-Box Q(40) 40.749492 0.4373
McLeod-Li(40) 15.902004 0.9998
Turning Points 0.312263 0.7548
Difference Sign -0.454859 0.6492
Rank Test 0.506336 0.6126
Multivariate Q(5)= 9.65744
Significance Level as Chi-Squared(20)= 0.97397
Test for Multivariate ARCH
Statistic Degrees Signif
72.90 45 0.00530
Looking at the RATS' User Guide and your reply in other topics, you said the model is adequate when the MVQSTAT and MVARCHTEST are insignificant. According to that, is it my estimated model above is invalid? Or can I say my model is adequate because of the univariate diagnostics test results? If not, how can I improve my model to be adequate? I have tried to add lags to the VAR mean model, but it is still strongly rejected in MVQSTAT.
Another question: How to decide the mean model before estimating the BEKK model? From the VARMAGARCH.RPF, it says the GARCH with a VAR mean model is common and better than VARMA. In general, it is best to start with a small model and add lags until the model is adequate. So can I use VAR(1) mean model straight away at the beginning? And once the BEKK-GARCH is adequate, there is no problem of using the VAR(1) mean model. In other words, can I say if the estimated BEKK-GARCH model is adequate, which kind of mean model is not of interest?
Thanks,
Haoting