## BEKK and xreg

Discussions of ARCH, GARCH, and related models

### BEKK and xreg

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
maathews

Posts: 3
Joined: Fri Mar 16, 2012 3:36 pm

### Re: BEKK and xreg

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 Choleski 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.
TomDoan

Posts: 2720
Joined: Wed Nov 01, 2006 5:36 pm

### Re: BEKK and xreg

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

Posts: 3
Joined: Fri Mar 16, 2012 3:36 pm

### Re: BEKK and xreg

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?
maathews

Posts: 3
Joined: Fri Mar 16, 2012 3:36 pm

### Re: BEKK and xreg

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

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

Posts: 2720
Joined: Wed Nov 01, 2006 5:36 pm

### Re: BEKK and xreg

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} d08equation eq2 elec#constant us{1} elec{1} d08group ar1 eq1 eq2garch(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 BFGSConvergence in    72 Iterations. Final criterion was  0.0000068 <=  0.0000100Usable Observations                      1960Log Likelihood                     17822.4434    Variable                        Coeff      Std Error      T-Stat      Signif************************************************************************************1.  Constant                     -0.000045915  0.000028149     -1.63115  0.102859242.  US{1}                        -0.016064707  0.021258071     -0.75570  0.449829563.  ELEC{1}                      -0.010522108  0.004178792     -2.51798  0.011803064.  D08                          -0.000132403  0.000067646     -1.95730  0.050312505.  Constant                      0.000621421  0.000126052      4.92986  0.000000826.  US{1}                        -0.075177976  0.084428560     -0.89043  0.373233437.  ELEC{1}                      -0.005163233  0.019478259     -0.26508  0.790950348.  D08                          -0.000250829  0.000477407     -0.52540  0.599305199.  C(1,1)                       -0.000013271  0.000040613     -0.32677  0.7438427310. C(2,1)                       -0.001967562  0.000307320     -6.40232  0.0000000011. C(2,2)                        0.002807408  0.000227981     12.31421  0.0000000012. A(1,1)                        0.285236654  0.019688861     14.48721  0.0000000013. A(1,2)                        0.243535328  0.143024692      1.70275  0.0886148214. A(2,1)                        0.013676527  0.            004239661            3.22585  0.0012559815. A(2,2)                        0.093552928  0.037699436      2.48155  0.0130813416. B(1,1)                        0.976584331  0.006239203    156.52390  0.0000000017. B(1,2)                       -0.661956591  0.089329609     -7.41027  0.0000000018. B(2,1)                        0.033683220  0.006329181      5.32189  0.0000001019. B(2,2)                        0.192191860  0.052254456      3.67800  0.0002350720. D08                           0.000143509  0.000060603      2.36803  0.0178832521. D08                          -0.002288900  0.000732116     -3.12642  0.0017695022. D08                           0.000290012  0.000496423      0.58420  0.5590828223. CHEMICALS                    -0.034686122  0.            004110490           -8.43844  0.0000000024. CHEMICALS                     0.646463457  0.039246560     16.47185  0.0000000025. 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??
avalokita

Posts: 13
Joined: Mon Sep 19, 2011 3:36 am