Diagnostic test and mean model for BEKK-GARCH

[TomDoan]

See https://estima.com/docs/RATS%209%20User ... f#page=175

Dear Tom,
I have another question. While trying to estimate my BEKK model, I get the following error message if I include more than three variables in the system:
MV-GARCH, BEKK - Estimation by BFGS
NO CONVERGENCE IN 197 ITERATIONS. FINAL NORMED GRADIENT 0.00013
SUBITERATIONS LIMIT EXCEEDED.
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

And then it gives some output.Could you please throw some light on it?Please reply soon!

Thanks.
Regards.

[sanjeev]

Dear Tom,
I have two doubts on which I need clarification from you:
First, when I estimate my GARCH-BEKK model with three variables in total, I find that changing the order of second and third variables changed the results.Could you help me find why it is so?
Secondly, when I look at my results, I find that in the mean equation,sign of the coefficient of a variable doesn't conform to the economic theory. Could you tell me what I should do in such a situation?
Please reply! Its very urgent.

Thanks.
Regards.

[sanjeev]

Dear Tom,
Thanks for your reply!
I am going through the user's guide you have suggested.But meanwhile can I ask you another related question?
Could the number of observations also be a reason for such output? I have annual data with only 35 observations.

Thanks.
Regards.

See https://estima.com/docs/RATS%209%20User ... f#page=175

Dear Tom,
I have another question. While trying to estimate my BEKK model, I get the following error message if I include more than three variables in the system:
MV-GARCH, BEKK - Estimation by BFGS
NO CONVERGENCE IN 197 ITERATIONS. FINAL NORMED GRADIENT 0.00013
SUBITERATIONS LIMIT EXCEEDED.
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

And then it gives some output.Could you please throw some light on it?Please reply soon!

Thanks.
Regards.

[TomDoan]

35 annual observations is barely enough to estimate a one lag VAR on more than three variables. You probably have maybe 10% of the data that would be necessary to estimate a 4 variable BEKK. Annual data almost never even shows GARCH properties at all.

[sanjeev]

Dear Tom,
Thanks for your reply!
I have two more doubts on which I need clarification from you:
First, when I estimate my GARCH-BEKK model with three variables in total, I find that changing the order of second and third variables changed the results.Could you help me find why it is so?
Secondly, when I look at my results, I find that in the mean equation,sign of the coefficient of a variable doesn't conform to the economic theory. Could you tell me what I should do in such a situation?
Please reply! Its very urgent.

Thanks.

[TomDoan]

Is this the same data set with 35 observations? That's nowhere near enough data to fit a 3 variable BEKK.

[sanjeev]

Dear Tom,
Yes it is.Then what is the maximum number of variables I can take in my model,only two? Actually I have come across papers that have fitted a 2 variable GARCH-BEKK model on annual data (Please find the link below for the relevant paper).But given my specification, I have to include at least three variables in the model. Could you help me?

https://link.springer.com/article/10.10 ... 014-9284-4

Thanks. Regards.

[TomDoan]

With 35 annual observations, probably one variable, and even that would be questionable. Because GARCH is attempting to infer behavior about an unobservable (the volatility), you need a lot of data as only "outliers" can actually give you any useful information about volatility persistence.

[sanjeev]

Dear Tom,
I am wondering if the signs of the coefficients in the mean and or variance equations matter in a GARCH-BEKK model. As in should they conform to the economic theory?
Please reply!

Thanks.

[TomDoan]

Since BEKK coefficients (a) aren't structural and (b) have signs that aren't identified statistically, I'm not sure what you mean by theoretical values.

[sanjeev]

Dear Tom,
Could you please send me the code for causality tests in mean and variance in GARCH-BEKK models?

Thanks and Regards.

[TomDoan]

See https://estima.com/docs/RATS%2010%20Use ... f#page=334

[sanjeev]

Referring to your response below, could you please make it clear as to how exactly one can incorporate the dummy in the mean model.
I tried the following but all in vain:

garch(p=1,q=1,model=var1,regressors,mv=bekk,pmethod=simplex,piters=20,iters=700,stdresiduals=rstd) / x1 x2 x3
# z
With this, the output window gives me mean and variance equations without the exogenous variable,z.And it says expected intruction here.
However, when I give the option xreg in the above code for GARCH, then I get coefficients for variable z in my variance equations(only).
Please respond!

Thanks.

Hi,
I want to incorporate dummy variables to account for structural breaks in my model.Could you help me do that? My precise question is how do we incorporate an exogenous variable in our model.
Please reply soon!
Thanks.

If it's a variance shift, it's with the XREG option. If it's a mean shift, you just incorporate it into the mean model. It would help if you could be more specific about what the exogenous variable is supposed to fix.

The mean model comes in as VAR1. In the definitions of the VAR1 system, add your dummy to the DETERMINISTIC list.

[sanjeev]

Also in continuation with my previous mail, with the codes I am currently using,I get mean and variance equations separately from the VAR equations.Can you let me know if and how we can get both the VAR model and the mean and variance equations simultaneously?
Please reply!
Thanks.

[TomDoan]

Also in continuation with my previous mail, with the codes I am currently using,I get mean and variance equations separately from the VAR equations.Can you let me know if and how we can get both the VAR model and the mean and variance equations simultaneously?
Please reply!
Thanks.

I have no idea what you mean. They are estimated simultaneously.