negative coefficients of ARCH terms in MGARCH-BEKK

[prashantj]

Dear Tom,

I have found volatility course material very useful. It is indeed great effort!
I am trying to estimate MVGARCH-BEKK representation to analyze volatility spillover between Exchange rate and stock market data. I have some doubt.
I find that "A()" coefficient value is turning out to be negative. Usually, I understand that the ARCH coefficient is expected to be positive. Is possible to get the negative value? Can you please guide me how to interpret it? I have attached the output for your reference, please.
Looking forward for your reply,
Prashant

[prashantj]

Dear Tom,
when I added one more variable and tried to estimate MVGARCH-BEKK. I got the following message.

MV-GARCH, BEKK - Estimation by BHHH
NO CONVERGENCE IN 4 ITERATIONS
LAST CRITERION WAS 0.0000000
SUBITERATIONS LIMIT EXCEEDED.
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK
Usable Observations 1032
Log Likelihood -4487.2417

I have estimated several time using various options like "INITIAL=%BETA and changed the method from "BFGS TO BHHH but of no avail. I obtained consistently the above message. could you please help?, please
Then I tried with two variables dropping one( "bse" in my dataset). The output (twovariable.rpf) is attached. The value of asymmetry coefficient is very large..58.60..I think it cannot be such large.honestly, i am confused..
I attach the programme, output and data set for your reference.
looking forward for your reply,
Regards,
Prashant

[TomDoan]

Those are probably converged as best you can get. Why are your last two variables almost identical? Your BEKK model is collapsing because the C matrix is effectively rank two.

[prashantj]

last two variables are bse and nse which are different. since BEKK model is collapsing because C matrix is rank two..How do I get rid of it? any solution?
prashant

[TomDoan]

They're almost identical. Graph them.

To fix it, don't run a GARCH model with two almost identical series.

[prashantj]

thanks..I plot the raw series of "sp.xls" attachment..their values are very different but they move together very much..The variables values are values of two different stock exchanges of india..

anyway..my another questions is can the coefficients A, B and D be negative? I get lots of negative values of the coefficients in different data. What could be the reason? does it make any difference?
Prashant

[TomDoan]

There's nothing wrong with negative coefficients in a BEKK model. This is discussed in considerable detail in the GARCH course on pp 92-93.

[prashantj]

Dear Tom,
thanks for your reply. I read page no 92-93. Nice discussion..thanks..

To refine my understanding,

If coefficients of D is negative, i interpret it as the following:

"The negative sign of D coefficients indicate that asymmetric volatility is affected more when it moves in opposite direction than in the same direction." I guess this is true for negative coefficients of A and G.
Am I correct? This will help me a lot..

Regards,
Prashant

[TomDoan]

What's G? I'm not sure what you're asking about A. Your "quote" is a paraphrase of a statement out of the course that was about A. (By the way, don't show as a quote something that isn't a quote).

The asymmetry terms in the BEKK only apply to linear combinations where the residuals are all negative, so what you wrote can't be correct. With an asymmetric BEKK model, there's no relatively simple interpretation of either A or D coefficients because of the way the two of them interact. This is discussed on pp 114-115.

[prashantj]

Then what should be the interpretation of negative coefficient of asymmetric coefficient (D) and GARCH coefficient(G) in BEKK output. I found the interpretation of negative coefficients of A on page 92-93 in GARCH book of volatility course. I attach the output which shows that some coefficients of GARCH and Asymmetric volatility (D) are negative. I am sorry to disturb you but honestly I am confused.
Looking forward for your reply,
Prashant

[TomDoan]

You're running the model with those two almost identical series. You have exactly the type of problem that you would have with any sort of near-perfect collinearity between regressors---the individual coefficients are poorly estimated and have no reasonable interpretation.

[prashantj]

That is making sense.

I found GARCH coeffient in example given in volatility course was negative. And in some case suppose in genuine series if GARCH and asymmetric coefficients--D are negative, what do they convey?
Prashant

[TomDoan]

To repeat: With an asymmetric BEKK model, there's no relatively simple interpretation of either A or D coefficients because of the way the two of them interact. This is discussed on pp 114-115.

You can try experimenting with different combinations of positive and negative values for the components of u's to see what happens.

[John]

Tom,
I estimated a MVGARCH bekk model. But there is something strange about B matrix. B(1,1) is negative and if I multiply entire B matrix by (-1) then B(2,2) will be negative.
How can I interpret my model?
Is something wrong with estimated model?
Thanks for your help in advance.

Code: Select all

15. C(1,1)                        0.010725649  0.001209000      8.87151  0.00000000
16. C(2,1)                        0.003421986  0.002133517      1.60392  0.10873214
17. C(2,2)                        0.003662564  0.002468769      1.48356  0.13792601
18. A(1,1)                        0.234926302  0.081743181      2.87396  0.00405366
19. A(1,2)                        0.436410211  0.060815568      7.17596  0.00000000
20. A(2,1)                        0.307881112  0.087678516      3.51148  0.00044562
21. A(2,2)                        0.332928950  0.063877522      5.21199  0.00000019
22. B(1,1)                       -0.571121090  0.126218135     -4.52487  0.00000604
23. B(1,2)                       -0.756600961  0.084402557     -8.96419  0.00000000
24. B(2,1)                       -0.274047914  0.183833852     -1.49074  0.13603057
25. B(2,2)                        0.460738741  0.123934910      3.71759  0.00020114
26. D(1,1)                        0.317817552  0.201760378      1.57522  0.11520502
27. D(1,2)                        0.133098173  0.182900933      0.72771  0.46679335
28. D(2,1)                        0.352687455  0.302793753      1.16478  0.24410893
29. D(2,2)                        0.075659768  0.212344995      0.35631  0.72161151
30. Shape                         4.202109967  0.555093269      7.57010  0.00000000

[TomDoan]

Those results look a pair of series which have very weak if any GARCH behavior with a few outliers sprinkled in.