MGARCH Diagonal BEKK results & Volatility spillovers

[Kalec]

Hi

I have preformed a MGARCH under diagonal bekk. However, I do not know how to read the results from eviews.
I would like to test for volatility spillovers, please advise how I can read the result in this respect.

Below is the result I obtained from eviews.

Thanks a lot
kalec

bekk.rtf

(24.82 KiB) Downloaded 1635 times

[ibrahim]

I am facing the same problem. How can I interpret mgarch diagonal bekk results. How can estimate volatility spillover in e-views? I already used trivariate m-garch code posted in e-views forum but didn't interpret the results.?
Please, help!
It is really urgent!

[trubador]

If shocks from one market/asset increase the volatility in another market/asset, then it is called spillover effect. Therefore, estimated coefficents on the lag(s) of squared residuals of other mean equations measure the volatility spillover effects. Other coefficients of cross terms are mostly related to volatility transmission effects.

[james123]

I have done the same test, but it seems like that Eviews only give conditional variance, there does not include conditional co-variance. I also feel confuse about the results. I am estimating the bivariate BEKK, hence I only get A1(1,1) A1(2,2) , B1(1,1) and B1(2,2). But when I look the equation presentation, it says the co-variance for A1(1,2)= A1(1,1)*A1(2,2). Then I think maybe we need to perform a Wald coefficient test in order to test the corvariance(volatility spillover). But I am not sure it is correct or not.

[james123]

Maybe this is the reason to call the Diagonal BEKK, not the original BEKK. Due to reduce the amount of the coefficients. I guess.

[nicktz]

Hi Trubador,

regarding the volatility spillover effects using the built in function (diagonal BEKK with indefinite matrix from the system window), I have the following query:
You mentioned: "Estimated coefficents on the lag(s) of other conditional volatilities are the spillover effects...", but in the representations window it is not clear that the lagged coefficients (i.e. M(1,2), M(1,2), M(2,3), etc) enter the GARCH equations to measure the spillover in the GARCH system?

It merely shows covariance in the system. Or am I misunderstanding the process here? In other words, can we measure whether past residuals of eq1 enter significantly the garch process of eq2 using this technique?
Also, is the spillover ordering here from eq 3 -> eq2 -> eq1 (or y3 -> y2 -> y1)?

One last thing, someo
Thanks for the help!

[trubador]

Diagonal versions do not allow for dynamic dependence among the volatility series. However, you can write your own (unrestricted) model via LogL object. Please search the forum for more details...

[nicktz]

Thanks for your prompt response!! I have searched the forum quite extensively for this but cannot seem to find a suitable discussion. I want to teach the spillover techniques to our students and really want to use Eviews for this. Do you have any suggestions of forum links?

[nicktz]

I.e. is there a link/ available technique on how to make A and B lower triangular matrices, i.e. include A(2,1), A(3,1), A(3,2) & B(2,1), B(3,1) B(3,2) to allow tests of volatility spillover?

[trubador]

The example of upper triangular version for the "-in mean" specification might give you the idea: viewtopic.php?f=4&t=3358#p11338

[nicktz]

Hi Trubador,
this question on the restricted version of BEKK has been posted several times (e.g. viewtopic.php?f=4&t=3355) and your advice has been to consult these forums: viewtopic.php?f=15&t=3364 and viewtopic.php?f=4&t=3358#p11338.
The problem is, in those examples of restricted versions the Omega (constant) matrix is upper triangular. I am wondering whether there is any code for the alpha and beta matrices to be lower triangular.
The dynamics are very much different for the programming (especially for the var_y1 and covar_y1y2), of which I have limited experience in Eviews, although I would like to use the program for lecturing on these topics.
Please help, as the User Guide II merely says on p456: "Eviews does not estimate the general form of BEKK where A and B are unrestricted". I am puzzled as to why this is the case?!
This is a serious shortcoming as one cannot then conduct meaningful volatility spillover analysis using GARCH modelling in Eviews.

Thank you for your help!

[trubador]

I don't know how urgent the matter is, but I'll look into it when I find some spare time...

[nicktz]

Thanks a lot Trubador, much appreciated! I have tried programming a lower triangular matrix system for the bivariate case (so that volatility in y2 spills over to y1) - but it doesn't seem to work.
It keeps saying: "Missing values in @Logl". It's probably some little coding error- would you mind checking if my approach is right and where I may have made a mistake?
Thanks a lot!

And if you could provide an unrestricted (or even similar lower triangular system) Trivariate BEKK Garch version in the future it would really help us a lot!

Thanks for the good work!

[nicktz]

Hi Trubador,

I found the mistake, I didn't square the beta coefficient! Getting a hang of programming in Eviews at last!

Do you mind just quickly checking that my code is correctly testing BV spillover from Y2 -> Y1, while not allowing spillover from Y1 -> Y2?
Also, is it correct to include the following line of coding at the bottom to use as a DCC series: "series rho12 = cov_y1y2/(@sqrt(var_y1)*@sqrt(var_y2))"

Thanks for your help, and please let me know if you find time to look at the Full Bekk-garch version.
Thanks!

[trubador]

Just to make things clear, you are also trying to capture the garch-in-mean effects. Having said that:
1) First univariate garch-m equation (eq1) did not converge,
2) Number of max iterations in all your equations are set to 100, which might not be enough in such complicated models,
3) In the following part of your code, replace garch1 and garch2 with var_y1 and var_y2, respectively:

Code: Select all

...
' squared errors and cross errors
bvgarch.append @logl logl
bvgarch.append sqres1 = (y1-mu(1)-lambda(1)*garch1)^2
bvgarch.append sqres2 = (y2-mu(2)-lambda(2)*garch2)^2
bvgarch.append res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)
...

4) Nothing is wrong with your rho12 specification since it is the definition of correlation. However, you should keep in mind that actual DCC-type models handle the correlation explicitly.