negative coefficients of ARCH terms in MGARCH-BEKK

[John]

Thank you Tom for your reply.
But MV ARCH TEST shows that lack of ARCH is overwhelmingly rejected (after estimating a VECM ):

Code: Select all

Test for Multivariate ARCH
Statistic Degrees Signif
  1328.52      27 0.00000 

Is my model incorrect?

[TomDoan]

You're interpreting the test backwards. That rejects lack of independence in the higher moments. It does not accept that "ARCH" effects are actually present.

[John]

sorry Tom, but in the page 80 of the GARCH course, in the interpretation of the @mvarchtest test (below) it is said that "which produces the (unsurprising) result that lack of ARCH is overwhelming rejected:
Test for Multivariate ARCH
Statistic Degrees Signif
370.11 36 0.00000

I just followed the steps of the GARCH course. At first, I estimated a VECM model and then I tested for ARCH effect with this result:
Test for Multivariate ARCH
Statistic Degrees Signif
1328.52 27 0.00000

And finally, I tried to correct ARCH efffet with a BEKK -VECM. But the results shows that B(1,1) is negative and B(2,2) positive. Therefore my question was why B(1,1) was negative.

[TomDoan]

The data in the GARCH workbook show signs of being governed by a well-behaved GARCH process with the proper type of volatility clustering and the estimated GARCH models confirm that. You have data which obviously don't exhibit either.

[John]

Tom,
I estimated a DCC model. It is converged. The results are good but DCC(A)+DCC(b) is just one. Does it mean that my model is incorrect? Here is results:

Code: Select all

MV-DCC GARCH  with Spillover Variances - Estimation by BFGS
Convergence in     2 Iterations. Final criterion was  0.0000000 <=  0.0000000
Usable Observations                       522
Log Likelihood                      2883.5691
13. C(1)                          0.000078670  0.000010045      7.83182  0.00000000
14. C(2)                          0.000056698  0.000007006      8.09306  0.00000000
15. A(1,1)                        0.177066005  0.034949264      5.06637  0.00000041
16. A(1,2)                        0.208418508  0.046066373      4.52431  0.00000606
17. A(2,1)                        0.220274610  0.028410876      7.75318  0.00000000
18. A(2,2)                        0.347364492  0.042049474      8.26085  0.00000000
19. B(1)                          0.559359066  0.021224966     26.35383  0.00000000
20. B(2)                          0.398261374  0.023298455     17.09390  0.00000000
21. D(1)                          0.161457879  0.069974239      2.30739  0.02103307
22. D(2)                         -0.251585415  0.065996126     -3.81212  0.00013778
23. DCC(A)                        0.017147413  0.001276756     13.43045  0.00000000
24. DCC(B)                        0.982852587  0.000843829   1164.75304  0.00000000
25. Shape                         4.016835788  0.313765837     12.80202  0.00000000

Multivariate Q(10)=      50.61471
Significance Level as Chi-Squared(40)=       0.12127

Test for Multivariate ARCH
Statistic Degrees Signif
    20.98      27 0.78707

[TomDoan]

You probably overdid the simplex iterations---the standard errors from 2 iterations of BFGS won't be valid.

Assuming you have data with a few big outliers, I'm not sure DCC actually will work well, particularly if the two series have outliers that aren't at the same location. DCC coefficients summing to one means that there is no "natural" correlation between the residuals of the two series---it drifts pretty much without bound over the data set.

[John]

I really appreciate your help Tom. I have just another question.
If in a bekk model the sum of A(1,1) and B(1,1) is greater than one, will it mean that the model is incorrect? (Just like a simple univariate GARCH model)
And If in a bekk model c(2,2) is negative but insignificant, will it mean that the model is incorrect?

Thank you very much.

[TomDoan]

I really appreciate your help Tom. I have just another question.
If in a bekk model the sum of A(1,1) and B(1,1) is greater than one, will it mean that the model is incorrect? (Just like a simple univariate GARCH model)
And If in a bekk model c(2,2) is negative but insignificant, will it mean that the model is incorrect?

Thank you very much.

Since the A's and B's get "squared", you can't say anything about this from the sum of coefficients. Nor can you say anything from the sum of squares---the stability condition depends upon the entire A and B matrices.

Regarding C, no. That just means that C is rank one, which is possible.

[prashantj]

When I choose t-errors and estimate BEKK MGARCH, the D coefficients are turning out to be statistically significant as follows:
GARCH(P=1,Q=1,MV=BEKK,DIST=T,ASYMMETRIC) / RBGCI RSPX

And when I use the following command, The D coefficients are insignificant. I do not know why it is and which one is correct.
garch(mv=BEKK,rvectors=rd,hmatrices=hh,pmethod=simplex,asymmetric,robusterrors,stdresids=rstd,piters=20,iters=500) / rbgci rspx

MGARCH.jpg (415.22 KiB) Viewed 12478 times

[TomDoan]

I'm going to guess that you have some really serious issues with your data. You don't get a t of 2.79 (it has to be bigger than 2) without some really huge outliers that can't be explained by the GARCH recursion.

[prashantj]

This is what I got when I use the following after adjusting for outliers.
garch(mv=BEKK,rvectors=rd,hmatrices=hh,pmethod=simplex,stdresids=rstd,piters=20,iters=500) / rbgci rspx

MGARCH.jpg (159.32 KiB) Viewed 12474 times

MGARCH diagonstic test suggests model is good fit. I think it is a good model?

[TomDoan]

No it doesn't. It's a terrible fit---look at the log likelihood difference between the model with t errors and this one. Tests for serial correlation (either in the mean or in second moments) will basically always "pass" if applied to a series with isolated outliers (the standing assumptions underlying those tests don't allow for outliers, so the tests don't behave properly in the presence of them).

[prashantj]

Thanks. How to deal with outliers in MGARCH? is better to use t-error model or GED better? or just remove the outliers. Mine is intraday data. How to deal with the outlier? please guide. Does help manual or GARCH course include it?
Prashant

[TomDoan]

Before you decide that, you have to figure out what the source of the problems are. If it's intraday data and it doesn't trade 24 hours a day, one assumes that there can be big differences between the end of one day and the start of the next; in which case, you need to use a more complex model, since a GARCH model which treats every observation identically isn't correct for that. Sometimes there are typos; sometimes there are phantom prices that don't represent any actual trades (for instance, if a circuit breaker prevents a price from moving too fast, typically no transactions will be made at the capped price). This is your data set and it's your job to figure out how it works.

[prashantj]

Thanks. I used the daily data and estimated the model. I have got the following. It sounds better model but still not sure. still outlier a problem?

spillover1.jpg (234.04 KiB) Viewed 12462 times