BEKK and xreg

[maathews]

How does xreg of a dummy variable enter into the bekk model?

Considering a 2 asset case, is it a hadamard product of a 2x2 parameter matrix and 2x2 dummy matrix. Or is it more complicated than this? i.e. bekk parameterization on the dummy?

Thanks

[TomDoan]

BEKK and dummies are a bit of a dilemma. Ordinarily, it doesn't matter whether you use 1 and D where the D measures the differential effect or 1-D and D where the coefficients are on separate subsamples. However, those aren't the same if you force the coefficients to be positive and they really aren't the same if you force them to have coefficients which are positive definite matrices. What we do with BEKK and GARCH is to add a Cholesky factor of the additive variance (similar to what is done with the variance model constant) and add its outer product x the dummy to the variance. So you want to make sure that you choose the dummy so that the observations to which it applies have a higher (addition to the) variance than those to which it doesn't.

[maathews]

Thanks for your reply.

To better understand this, given the dummy gives 3 parameter estimates for the output in rats. How would I add these coefficients to the long-run conditional covariance (Constant) terms to see the change? Would it be similar to the C'C matrix? i.e. d1sq, D1D2, D2sq + D3sq?

[maathews]

All I really need to know is if cross-regressors (1 simple dummy) are parameterized in the same way as you would a BEKK-asymmetric (tgarch) specification...

Or if it is just "added" onto each equation, hence it would be just a hadamard product of a 2x2 parameter matrix and a 2x2 dummy matrix.

My problem is probably addressed somewhere, but I cannot seem to find it, can anyone link to me a source or post?

[TomDoan]

The variance is H(t)=CC'+FF' x D(t)+...

where F is lower triangular. A Hadamard product wouldn't maintain forced positive definiteness.

[avalokita]

Dear Tom:

Let's take an example from the other forum, in which codes look like as follows:

Code: Select all

equation eq1 us 
#constant us{1} elec{1} d08
equation eq2 elec
#constant us{1} elec{1} d08

group ar1 eq1 eq2

garch(p=1,q=1,model=ar1,mv=bek,XREGRESSORS,pmethod=simplex,piters=10,hmatrices=hh,rvectors=rr) / us elec
# D08 chemicals

Results are shown as:

Code: Select all

MV-GARCH, BEKK - Estimation by BFGS
Convergence in    72 Iterations. Final criterion was  0.0000068 <=  0.0000100
Usable Observations                      1960
Log Likelihood                     17822.4434

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Constant                     -0.000045915  0.000028149     -1.63115  0.10285924
2.  US{1}                        -0.016064707  0.021258071     -0.75570  0.44982956
3.  ELEC{1}                      -0.010522108  0.004178792     -2.51798  0.01180306
4.  D08                          -0.000132403  0.000067646     -1.95730  0.05031250
5.  Constant                      0.000621421  0.000126052      4.92986  0.00000082
6.  US{1}                        -0.075177976  0.084428560     -0.89043  0.37323343
7.  ELEC{1}                      -0.005163233  0.019478259     -0.26508  0.79095034
8.  D08                          -0.000250829  0.000477407     -0.52540  0.59930519
9.  C(1,1)                       -0.000013271  0.000040613     -0.32677  0.74384273
10. C(2,1)                       -0.001967562  0.000307320     -6.40232  0.00000000
11. C(2,2)                        0.002807408  0.000227981     12.31421  0.00000000
12. A(1,1)                        0.285236654  0.019688861     14.48721  0.00000000
13. A(1,2)                        0.243535328  0.143024692      1.70275  0.08861482
14. A(2,1)                        0.013676527  0.            004239661            3.22585  0.00125598
15. A(2,2)                        0.093552928  0.037699436      2.48155  0.01308134
16. B(1,1)                        0.976584331  0.006239203    156.52390  0.00000000
17. B(1,2)                       -0.661956591  0.089329609     -7.41027  0.00000000
18. B(2,1)                        0.033683220  0.006329181      5.32189  0.00000010
19. B(2,2)                        0.192191860  0.052254456      3.67800  0.00023507
20. D08                           0.000143509  0.000060603      2.36803  0.01788325
21. D08                          -0.002288900  0.000732116     -3.12642  0.00176950
22. D08                           0.000290012  0.000496423      0.58420  0.55908282
23. CHEMICALS                    -0.034686122  0.            004110490           -8.43844  0.00000000
24. CHEMICALS                     0.646463457  0.039246560     16.47185  0.00000000
25. CHEMICALS                     0.314006090  0.054514870      5.76001  0.00000001

So these X REGRESSORS (20-22 D08) correspond to elements f11, f21, f22.
Is my interpretation right??