The RATS Software Forum

Dear All,

Can we have the variance equations used in standard unrestricted GARCH model used by ESTIMA.

This is because there is difference in the BEKK-GARCH model equation by equation

i.e. pg no 5/18 of the paper "The importance of oil assets for portfolio optimization: The analysis of firm level stocks "

versus

pg no 3/7 of the paper " Volatility spillover effects in leading cryptocurrencies: A BEKK- MGARCH analysis"

Why is there differences here ?

The "sandwich" calculations in the BEKK model can be written in either the form BHB' or B'HB without changing the properties or the likelihood. The first paper you cite uses the first form, the second uses the second form. The original BEK paper used the second form, and I suspect that the authors would like a "do-over" on that, as it's not as natural. However, most papers (and probably most software, including RATS) use the original form.

Dear Tom,

Thanks a lot for the prompt clarification.

1) How can we extract the variance equations used when we run the bivariate BEKK command in RATS. I mean we do get the BEKK model output, but i also want to see all variance equations which went behind. Will also help me in better understanding of the process.

2) k12,t and k22,t represent the conditional variance of pakistan stock returns and conditional variance between oil returns and pakistan stocks,on pg no 5/18 of the paper "The importance of oil assets for portfolio optimization: The analysis of firm level stocks " . But should it not be the other way round ?

vicky007 wrote:Dear Tom,

Thanks a lot for the prompt clarification.

1) How can we extract the variance equations used when we run the bivariate BEKK command in RATS. I mean we do get the BEKK model output, but i also want to see all variance equations which went behind. Will also help me in better understanding of the process.

You have that backwards. The quadratic forms are the structural equations which define the BEKK variance evolution. The expanded equations really don't tell you much. However, you can get the VECH representation (which is basically what those are showing) by using the VECHMAT option on GARCH.

vicky007 wrote: 2) k12,t and k22,t represent the conditional variance of pakistan stock returns and conditional variance between oil returns and pakistan stocks,on pg no 5/18 of the paper "The importance of oil assets for portfolio optimization: The analysis of firm level stocks " . But should it not be the other way round ?

Yes. They have k12 where they need k22 and vice versa.

TomDoan wrote:

vicky007 wrote:Dear Tom,

Thanks a lot for the prompt clarification.

1) How can we extract the variance equations used when we run the bivariate BEKK command in RATS. I mean we do get the BEKK model output, but i also want to see all variance equations which went behind. Will also help me in better understanding of the process.

You have that backwards. The quadratic forms are the structural equations which define the BEKK variance evolution. The expanded equations really don't tell you much. However, you can get the VECH representation (which is basically what those are showing) by using the VECHMAT option on GARCH.

Dear Tom,

I am studying spillover between australia and brazil stock market returns (daily) in file attached tab "mydatadailyreturns" between 10/9/2008 to 31/12/2018. I have really tried hard over the past few days to be able to generate the variance equations (h11, h22, h12) by VECHMAT , so that i can understand them and also calculate the weights for hedge ratios. Can you please help me out in this and share the modified code which i can use to get the

h11 = conditional variance of australian stock returns
h22 = conditional variance of brazil stock returns
h12=h21 = conditional covariance between australian and brazil stock returns

Currently i am using the following code

GARCH(P=1,Q=1,MV=BEKK,robusterrors,stdresids=rstd,DIST=GED) / Australia Brazil
@REGCRITS
@mvqstat(lags=10)
# rstd
@mvarchtest(lags=2)
# rstd


Thanks in advance. The sample output from another study i trying to replicate is in the second tab "sampledataofstudyitryingtorepli" for your reference which shows daily variance and covariance being used for weights/hedging. So if you can share the modified code to get the conditional variance/covariance with my code, i will be obliged

The GARCH instruction is already computing everything you need. (It has to---the likelihood depends upon the conditional covariance matrix). Use the HMATRICES option on GARCH. If you follow the thread below, it shows how to compute the portfolio weights and hedge ratios using RATS.

https://estima.com/forum/viewtopic.php?f=11&t=3220

If you still want to get the information over into the spreadsheet you can use the MVHSERIES option, which gets the conditional variances and covariances as series. You can then do a COPY or PRINT instruction to get access to those so you can move them to Excel.

GARCH(P=1,Q=1,MV=BEKK,robusterrors,stdresids=rstd,mvhseries=mvh,hmatrices=hh,DIST=GED) / Australia Brazil
print(window="Conditional Cov") / mvh(1,1) mvh(2,2) mvh(1,2)

I am studying spillover between australia and brazil stock market returns

Note that hedge ratios and portfolio weights tell you nothing about "spillover"---the returns can be conditionally correlated (which will give you non-trivial hedge ratios) without any special dynamic relationship in the volatility.