Asymmetric Trivariate GARCH BEKK for Volatility Spillovers

[elisabettac]

Hi all,

I am trying to replicate in RATS the model adopted by Li and Giles in their paper "Modelling Volatility Spillover Effects Between Developed Stock Markets and Asian Emerging Stock Markets" to estimate volatility spillovers between three different markets.

I am using their same data but I am having some difficulties obtaining the same results. I have found ln*100 returns of three different markets and then used the Multivariate GARCH Wizard, selecting BEKK Model type, specifying as dependent variable the three markets analysed and ticking the box of asymmetric effects.
What other steps should I take?

I am a beginner user of RATS so any kind of help is really more than appreciated!
Thank you

Note: You can find the aforementioned paper at this link: https://www.researchgate.net/publicatio ... CK_MARKETS

[TomDoan]

It sounds like you are missing the dynamics in the mean model---they're using a 4 lag VAR, which is very important in this case because of the timing of the different markets. You can do that with the wizard by putting in the lags (in addition to the CONSTANT) into the Mean Model Variables, though it's probably easier to set up a model for the mean and put that into the GARCH model. See, for instance, VAR(1) example in the GARCHMV.RPF example:

*
* VAR(1) model for the mean, BEKK for the variance
*
system(model=var1)
variables xjpn xfra xsui
lags 1
det constant
end(system)
*
garch(p=1,q=1,model=var1,mv=bekk,pmethod=simplex,piters=10)

[elisabettac]

It sounds like you are missing the dynamics in the mean model---they're using a 4 lag VAR, which is very important in this case because of the timing of the different markets. You can do that with the wizard by putting in the lags (in addition to the CONSTANT) into the Mean Model Variables, though it's probably easier to set up a model for the mean and put that into the GARCH model. See, for instance, VAR(1) example in the GARCHMV.RPF example:

*
* VAR(1) model for the mean, BEKK for the variance
*
system(model=var1)
variables xjpn xfra xsui
lags 1
det constant
end(system)
*
garch(p=1,q=1,model=var1,mv=bekk,pmethod=simplex,piters=10)

Hi Tom,
Thank you for your answer. I tried to set up the model for the VAR(4), but still I did not obtain the results showed in the paper. Also, many of the results I obtained are statistically insignificant where they are not in the paper. Would you have other suggestions?

Below there's the code I have used:
SYSTEM(MODEL=VAR4)
VARIABLES SP500 TOPIX JAKARTA
LAGS 1 TO 4
DET Constant
END(SYSTEM)
*
GARCH(P=1,Q=1,model=var4,MV=BEKK,ASYMMETRIC,ITERS=10000,pmethod=simplex,PITERS=10) / SP500 TOPIX JAKARTA

Thank you so much for your help.

[TomDoan]

You would have to attach the data set (and the full program would be helpful as well).

[elisabettac]

You would have to attach the data set (and the full program would be helpful as well).

Thank you.
This is the full program:

OPEN DATA "/Users/E/Desktop/DATA (SP500 TOPIX JAKARTA).xlsx"
CALENDAR(7) 1993:1:1
DATA(FORMAT=XLSX,ORG=COLUMNS,SHEET="RETURNS") 1993:01:01 2012:12:31 SP500 TOPIX JAKARTA
*
SYSTEM(MODEL=VAR4)
VARIABLES SP500 TOPIX JAKARTA
LAGS 1 TO 4
DET Constant
END(SYSTEM)
*
GARCH(P=1,Q=1,model=var4,MV=BEKK,ASYMMETRIC,ITERS=10000000,pmethod=simplex,PITERS=10) / SP500 TOPIX JAKARTA


For the data, I am attaching a file with 4 tabs:
- the first 3 tabs contain the prices as downloaded from Datastream (so the list of dates includes only trading days).
- the fourth tab contains the returns, computed on Excel as 100*ln(P(t)/P(t-1)) and the dates have been adjusted to display all the days of the years, with returns over non-trading days equal to zero.

[TomDoan]

Is this their dataset or is this your attempt to reconstruct their data set? This data file includes weekends.

[elisabettac]

Is this their dataset or is this your attempt to reconstruct their data set? This data file includes weekends.

This is my attempt to reconstruct the data. Attached I also send the version with returns over weekdays only (tab 5), which still does not yield the same results as in the paper.

Thank you

[TomDoan]

I have no idea where they get their results. The very large (for this type of model) first lag coefficients on SP500 in both equations for the other returns look implausible. What you're doing is correct.

[humyra]

Dear elisabettac,

I am new to RATS and investigating volatility spillovers between different financial markets. I wanted to know how you have treated non-trading days in one market due to a national holiday while the other market is open. I looked at your dataset in the attached file and saw that some of your weekday returns are zero. Am I right that you have assumed the same closing price on the holiday as the previous day so that return is zero? Is it possible for you share citations of some papers that have used the same approach?

Thank you.

[elisabettac]

Dear elisabettac,

I am new to RATS and investigating volatility spillovers between different financial markets. I wanted to know how you have treated non-trading days in one market due to a national holiday while the other market is open. I looked at your dataset in the attached file and saw that some of your weekday returns are zero. Am I right that you have assumed the same closing price on the holiday as the previous day so that return is zero? Is it possible for you share citations of some papers that have used the same approach?

Thank you.

Hi humyra,
Apologies for this late reply. Yes, for national holidays I have considered a return equal to zero as the stock market did not move from the closing price of the last trading day. I assume this is also the approach adopted in the paper by Giles and Li I mentioned in one of my previous posts here.
Hope this helps!

[humyra]

Thank you for your help!