Analyzing contagion between financial markets

[humyra]

Hi,

I am analyzing volatility spillovers between banks and different financial markets and have decided on a VAR(1)-BEKK-GARCH(1,1) model.

However, the two coefficients that I'm interested in (A12 and B12) have negative signs. How do I interpret this?

Also, the mvarchtest is also significant suggesting the ARCH effect is still there. How can I correct this?

I am thinking of two other models to run. ARMA-BEKK-GARCH and Assymetric VAR-BEKK-GARCH. Which would you recommend? Could you please also share the code for both models.

Thanks.

[TomDoan]

There is almost no situation where an ARMA mean model is better than a VAR mean model in doing a GARCH. See https://estima.com/ratshelp/varmagarchrpf.html.

There's no general reason to prefer an asymmetric BEKK over a symmetric. You would just have to see whether the asymmetric model gives a improved fit good enough to overcome the added parameters.

[humyra]

Thank you Tom.

This is the code I have run:

system(model=varmodel)
variables NordeaSS MXWO
lags 1
det constant
end(system)

garch(p=1,q=1,model=varmodel,mv=bekk,pmethod=simplex,piters=10,$
rseries=rs,hmatrices=hmat,stdresids=zu)

@mvqstat(lags=5)
# zu
@mvarchtest(lags=5)
# zu

@mvqstat(lags=40)
# zu
@mvarchtest(lags=40)
# zu

These are the results I obtain:

MV-GARCH, BEKK - Estimation by BFGS
Convergence in 60 Iterations. Final criterion was 0.0000028 <= 0.0000100

Daily(5) Data From 2005:01:05 To 2017:05:05
Usable Observations 3218
Log Likelihood -9343.0393

Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(NORDEASS)
1. NORDEASS{1} -0.136753219 0.019518733 -7.00625 0.00000000
2. MXWO{1} 0.268666847 0.040246684 6.67550 0.00000000
3. Constant 0.032514372 0.025372722 1.28147 0.20002877
Mean Model(MXWO)
4. NORDEASS{1} -0.003597799 0.009227702 -0.38989 0.69661710
5. MXWO{1} 0.129964144 0.020866251 6.22844 0.00000000
6. Constant 0.047847965 0.012537891 3.81627 0.00013548

7. C(1,1) 0.143956245 0.034877386 4.12750 0.00003667
8. C(2,1) 0.013672060 0.027098085 0.50454 0.61388217
9. C(2,2) 0.099332996 0.010271418 9.67082 0.00000000
10. A(1,1) 0.123196724 0.019711759 6.24991 0.00000000
11. A(1,2) -0.060642829 0.009943948 -6.09847 0.00000000
12. A(2,1) 0.301637501 0.044381072 6.79653 0.00000000
13. A(2,2) 0.361337698 0.017849718 20.24333 0.00000000
14. B(1,1) 0.988789954 0.006086743 162.44976 0.00000000
15. B(1,2) 0.015217262 0.004049040 3.75824 0.00017111
16. B(2,1) -0.076049564 0.017196282 -4.42244 0.00000976
17. B(2,2) 0.929537331 0.007067671 131.51960 0.00000000

Multivariate Q(5)= 22.16226
Significance Level as Chi-Squared(20)= 0.33177

Test for Multivariate ARCH
Statistic Degrees Signif
118.43 45 0.00000

Multivariate Q(40)= 163.44306
Significance Level as Chi-Squared(160)= 0.40970

Test for Multivariate ARCH
Statistic Degrees Signif
444.02 360 0.00164

I'm just unable to find an economic explanation for the negative sign of A12 as well as the significant Multivariate ARCH test. Should I conclude that VAR-BEKK-GARCH is not the correct model and run some other model?

Also, how can I apply the LB Qtest to the the standardized residuals and the standardized squared residuals from the VAR model?

Thanks.