The RATS Software Forum

Dear Tom,

I am trying to replicate the paper of Ng "Volatility spillover effects from Japan and the US to the Pacific–Basin". In this paper, first a bivariate ADC GARCH model was fitted and after this, the residuals were orthogonalised. In this paper some specification test were used to check the performance of the model. I am unable to code these specification tests. I am wondering if you can help me in this regards.

Thanks,

The paper is behind a pay wall. However, what specification tests is it doing that isn't covered in the GARCHMV example.

Edit: an example of estimating the bivariate GARCH model, doing the diagnostics and orthogonalizing the residuals is at

https://estima.com/forum/viewtopic.php?p=12761#p12761

Thanks for the reply.
The specification test null hypothesis is that the standardized residuals follow bi-variate normal distribution by examining the third and fourth moments i.e. skewness and excess kurtosis and cross skewness and cross excess kurtosis.
The tests are:
E(Z_(i,t)^3 )=0 for i=1,2
E(Z_(i,t)^2 Z_(j,t) )=0
E(Z_(i,t)^4 -3 )=0 for i=1,2
E(Z_(i,t)^2 Z_(j,t)^2 -1 )=0

Moment-based tests can be done with something like:

set testk1 = zu(1)^4-3
mcov(opgstat=zu1k)
# testk1
cdf(title="Test of kurtosis on standarized residual #1") chisqr zu1k 1

You can either do those on the statistics one at a time (as is done above) or jointly (multiple test series on the MCOV with an adjustment for the degrees of freedom). An OPG test does a "robust" estimate of the variance of the sum, and so won't be the same as a test which computes the expected values under the null of N(0,I) residuals the way that (for instance), the Jarque-Bera test does.

Dear Tom, I missed one point in my question. The standardized residuals were calculated using the cholesky decomposition of the covariance matix instead of the usual sqrt of the covariance. How does this have an impact on the specification test of the MGARCH models.

I'm not sure what you mean by "usual sqrt of the covariance". If the original paper simply divided residuals by their own standard deviation, then the cross variables tests that you give would be wrong. You have to do some form of joint standardization in order to do any cross variable testing, and each one will give different results on the diagnostics. That doesn't make any one of them "right" or "wrong". They're just different.

Dear Tom, Thanks for the explanation. I have uploaded the specification test section.

I'm not sure what that has to do with your previous question. Given the z-hats, you do the tests (individually and jointly) as I described above. Nothing in what you posted describes how *she* computes the z-hats. I assume that she's doing some form of joint standardization. There are many (reasonable) ways to do that, and each will give somewhat different results.

Dear tom,

I am trying to orthogonalize the residuals using cholesky decomposition in a bivariate DCC GARCH model. I have applied the following code for the process. Please let me know if this is the correct way to orthogonalize the data.
Kind Regards.

Why would you orthogonalize the data? As you have that written the ZS are the (Cholesky) orthogonalized residuals which is what you need for diagnostics.

Thanks for the reply. I want those residuals to use as an external regressor for another equation. can i use the standardize residuals as external residuals?

I guess that would depend upon what you want to do with them. I would be hard-pressed to think of how GARCH-standardized residuals would be a useful explanatory variable in an external model.

Please see the attached paper in which the orthogonal residuals are used as external regressors.

This does the generation of the orthogonalized residuals for the USA-Japan submodel that she uses in the small market models. Those are orthogonalized while leaving the levels intact. This doesn't use the typical Cholesky factor---rather than SS'=sigma, it factors as LDL'=sigma where L has 1's on the diagonal. The L matrix can be computed by doing the Cholesky factor and dividing each column by its diagonal element. The standardized residuals that are computed by the STDRESIDS option scale out the levels so they have (theoretically) unit variances as well. Those are useful for diagnostics (I've included the calculations of the moment-based diagnostics as well), but not for what she's doing in the small market models since the standardized residuals have lost the original units of the data.