BEKK Diagnostics

[luxu1983]

dear
this is result of my model
are this reslt valid:?:
thank you


MV-GARCH, BEKK - Estimation by BFGS
Convergence in 75 Iterations. Final criterion was 0.0000000 <= 0.0000010
With Heteroscedasticity/Misspecification Adjusted Standard Errors
Usable Observations 1076
Log Likelihood 9305.86046927

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. C(1,1) 0.000001448 0.000001250 1.15855 0.24663998
2. C(2,1) -0.002089220 0.000660558 -3.16281 0.00156254
3. C(2,2) -0.000000021 0.000794296 -2.59057e-05 0.99997933
4. A(1,1) 0.185336523 0.054522930 3.39924 0.00067573
5. A(1,2) -3.055001838 0.696314206 -4.38739 0.00001147
6. A(2,1) 0.000114818 0.000112631 1.01942 0.30800406
7. A(2,2) -0.234928084 0.037610981 -6.24626 0.00000000
8. B(1,1) 0.963274261 0.005900404 163.25565 0.00000000
9. B(1,2) 0.130584733 0.229036825 0.57015 0.56857778
10. B(2,1) -0.000000677 0.000018253 -0.03707 0.97042641
11. B(2,2) 0.957178902 0.013947873 68.62544 0.00000000
12. D(1,1) 0.259644666 0.044026865 5.89741 0.00000000
13. D(1,2) 0.540765047 1.275232631 0.42405 0.67152783
14. D(2,1) -0.000328218 0.000098339 -3.33761 0.00084503
15. D(2,2) 0.145319842 0.087379655 1.66309 0.09629531

[TomDoan]

Why wouldn't it be?

[luxu1983]

Why wouldn't it be?

are the mgarch process stationary?

[TomDoan]

And if it weren't...?

The likelihood function for a BEKK is computable whether or not the variance model is stationary. A very non-stationary model will almost certainly never fit well (the in-sample variance predictions will eventually fail to be close), so if it's non-stationary, it will only be slightly that way.

[luxu1983]

And if it weren't...?

The likelihood function for a BEKK is computable whether or not the variance model is stationary. A very non-stationary model will almost certainly never fit well (the in-sample variance predictions will eventually fail to be close), so if it's non-stationary, it will only be slightly that way.

Dear Tom
i think my model above fits well.
do you think so?

[TomDoan]

There's nothing obviously wrong with it, but it's impossible to tell if it's "good" based upon just that limited amount of information. How does it compare with a simpler model like CC: are the added parameters for BEKK worth it? Is asymmetry necessary? Do standardized residuals show any remaining ARCH effects?

[avalokita]

There's nothing obviously wrong with it, but it's impossible to tell if it's "good" based upon just that limited amount of information. How does it compare with a simpler model like CC: are the added parameters for BEKK worth it? Is asymmetry necessary? Do standardized residuals show any remaining ARCH effects?

Hi, dear Tom:

I'm new here and new to multivariate Garch, but very interested in relevant issues.
How to tell if a BEKK model fits well? What functions does Rats provide to test model adequacy?
When using LB test, how do we determine the optimal number of lags?
How we handle if we find serial correlations and remaining ARCH effects in the residuals?

I have read some papers and found a lot of variation in the examinations,
so i doubt the validity of these examinations.
It looks like you are an expert, (of course u r), thus, would you please give more comments?

Thanks in advance.

[TomDoan]

Hi, dear Tom:

I'm new here and new to multivariate Garch, but very interested in relevant issues.
How to tell if a BEKK model fits well? What functions does Rats provide to test model adequacy?
When using LB test, how do we determine the optimal number of lags?
How we handle if we find serial correlations and remaining ARCH effects in the residuals?

I have read some papers and found a lot of variation in the examinations,
so i doubt the validity of these examinations.
It looks like you are an expert, (of course u r), thus, would you please give more comments?

Thanks in advance.

The Tsay textbook examples are probably the best to look at for diagnostics. The two main diagnostics are the LB test and the McLeod-Li test, both applied to standardized residuals. There are both univariate and multivariate versions of each. You really don't need to test a large number of lags in either case since there is rarely anything you can do to fix correlations at long lags. A significant LB test means that your mean model is wrong; there's more dynamics in the model than you included. Typically, that would be fixed by adding lagged dependent variables (that is, using a VAR-GARCH). A significant McLeod-Li (LB on the squares) means that the GARCH part of the model is somehow inadequate. It's rather rare to add lags to a GARCH in an effort to fix that; instead, you might want to check into asymmetric effects or a different model type (such as an EGARCH). As I mentioned in the quote from the previous message, another check in the BEKK is whether it actually fits (significantly) better than a simpler CC model.

[avalokita]

Thank you for your instant reply!!!

Yeah, I'm reading the Tsay textbook and reviewing the programs provided by Estima.
The textbook mentions how to select the best lag orders for the LB test (n =ln T)
but doesn't explain too much about the degrees of freedom applied in chi-squared distributions.
The way Tsay calculated the degrees of freedom is different from Chris Brooks (Author of RATS Handbook to Accompany Introductory Econometrics for Finance).
I also feel confused about the programs due to the lack of comments on some codes.
Take tsayp365.prg (pre Version 6.1) for example,

Code: Select all

set ustdsq = ustd**2
corr(qstats,dfc=1,number=4) ustd
corr(qstats,dfc=2,number=4) ustdsq

I am at a loss about what determines the dfc value.
Tsay doen't give any bekk example using Rats (he uses S-plus) ,
what about the degrees of freedom when running a bekk model?
Is the LB test for univariate garch different from that for multivariate?

I may feel sorry if I ask any question which is trivial for the current Rats 8.

[TomDoan]

Thank you for your instant reply!!!

Yeah, I'm reading the Tsay textbook and reviewing the programs provided by Estima.
The textbook mentions how to select the best lag orders for the LB test (n =ln T)
but doesn't explain too much about the degrees of freedom applied in chi-squared distributions.
The way Tsay calculated the degrees of freedom is different from Chris Brooks (Author of RATS Handbook to Accompany Introductory Econometrics for Finance).
I also feel confused about the programs due to the lack of comments on some codes.
Take tsayp365.prg (pre Version 6.1) for example,

Code: Select all

set ustdsq = ustd**2
corr(qstats,dfc=1,number=4) ustd
corr(qstats,dfc=2,number=4) ustdsq

I am at a loss about what determines the dfc value.
Tsay doen't give any bekk example using Rats (he uses S-plus) ,
what about the degrees of freedom when running a bekk model?
Is the LB test for univariate garch different from that for multivariate?

I may feel sorry if I ask any question which is trivial for the current Rats 8.

The degrees of freedom correction on the squared residuals is the number of parameters whose goal it is to eliminate the "GARCH" effects. Those are two "GARCH" parameters (lagged variance, lagged squared residuals). The degrees of freedom on the standard BQ test will be the number of parameters that are there to reduce serial correlation. That would be the sum of the number of AR and MA elements in the mean model which here is 1.

Those are for univariate models. There is no theoretical result for the asymptotics of the McLeod-Li test applied to standardized residuals out of a BEKK, but a chi-squared with DFC=2 probably comes close.

[avalokita]

The degrees of freedom on the standard BQ test will be the number of parameters that are there to reduce serial correlation. That would be the sum of the number of AR and MA elements in the mean model which here is 1.

Dear Tom:
I'm very grateful for your help, but I am still unclear about one point.
There are two Garch models in tsayp365.prg (pre Version 6.1).

The first one:

Code: Select all

garch(p=1,q=1,reg,resids=hkres,hseries=hkvar) / hk
# hk{1}
*
* Diagnostics on the standardized residuals
*
set ustd = hkres/sqrt(hkvar)
set ustdsq = ustd**2
corr(qstats,dfc=1,number=4) ustd
corr(qstats,dfc=2,number=4) ustdsq
*

An ar(1)-garch(1,1) model, and so the dfc for ustd is one. That follows the rule.

But as for the second:

Code: Select all

garch(p=1,q=1,nomean,resids=jares,hseries=javar) / ja
set ustd = jares/sqrt(javar)
set ustdsq = ustd**2
corr(qstats,dfc=1,number=4) ustd
corr(qstats,dfc=2,number=4) ustdsq

The mean equation is simply with a disturbance component. Nor constant neither AR terms exist.
Is dfc = 1 for ustd still valid??

Another question is: What if the corr for squared residuals indicates significant remaining ARCH effects,
but ARCH-LM test doesn't find? How do we copy with??

Code: Select all

lin ustdsq
# constant ustdsq{1 to 4}
compute trsq = %nobs*%rsquared
disp 'ARCH LM test:'
cdf chisqr trsq 4

[TomDoan]

The ARCH test, when applied to the residuals from an ARCH, also should have a correction to the degrees of freedom. The McLeod-Li and ARCH autoregression tests should generally give fairly similar results.