Volatility Spillover results interpretation BEKK

[ek95]

Hello everyone,

I am trying to find volatilty spillovers,so I have two daily return series RINDEX and RETF. I calculated a BEKK GARCH model in WinRats with RINDEX and RETF as the dependent variables. How do I interpret the results? or is the methodology not suitable?
Thank you

[TomDoan]

See https://estima.com/newslett/Apr2019RATS ... pdf#page=3. Yes, BEKK models are what are usually used for "spillover" tests. As described in that article, the results of those can be somewhat misleading.

[curiousresearcher]

Dear Tom,

Can the covariance number between 2 cryptocurrencies from bekk (1,1) model be more than 1 or less than 1 on some dates

The output MVH(2,1) using the RATS codes in BEKK GARCH

Please tell as in my data for few emerging crptos it is coming out more than 10 on few days in a 5 year time frame.

[TomDoan]

1. I'm not sure what you mean by "on some dates". The coefficients are fixed across a sample.
2. MVH(2,1) sounds like you're doing a BEKK-GARCH-M model. The MVH coefficients show the effect the variances have on the mean, not the effect they have on the variances (the latter is the volatility spillover).

However, the cross coefficients in GARCH models depend upon relative scales of the data and relative scales of the variances, so there is no particular reason they can't be bigger than 1.

[curiousresearcher]

1. I'm not sure what you mean by "on some dates". The coefficients are fixed across a sample.
2. MVH(2,1) sounds like you're doing a BEKK-GARCH-M model. The MVH coefficients show the effect the variances have on the mean, not the effect they have on the variances (the latter is the volatility spillover).

However, the cross coefficients in GARCH models depend upon relative scales of the data and relative scales of the variances, so there is no particular reason they can't be bigger than 1.

Dear Tom,

What command should i use to replace MVH in case, i want to see the effect in variances (volatility spillover)

[TomDoan]

The test for variance spillovers in a BEKK is a test on coefficients in the BEKK matrices (the off-diagonal A's and B's)---you don't run a different model. That's described in the linked article. Again, as that points out, "spillover" may simply be an artifact of the choice of BEKK rather than a different multivariate GARCH model.

[curiousresearcher]

what does negative garch cross coeffecient mean = long term volatility in market A has a negative impact on long term volatility of market B / Or the situation can long term volatility in market A has a poisitive impact on long term volatility of market B.

Can you explain what is theoritical meaning /interpretation of positive or negative?

[TomDoan]

what does negative garch cross coeffecient mean = long term volatility in market A has a negative impact on long term volatility of market B / Or the situation can long term volatility in market A has a poisitive impact on long term volatility of market B.

Can you explain what is theoritical meaning /interpretation of positive or negative?

The "long-term" volatility is a complicated function of all the GARCH coefficients (the C's, A's and B's)---you can't tell much of anything from a single coefficient in isolation. If you're talking about the conditional volatility; no in a BEKK model the effect of one variance on another is always positive (the coefficients square). It's a fool's errand to try to interpret individual coefficients in a BEKK model.

[curiousresearcher]

what does negative garch cross coeffecient mean = long term volatility in market A has a negative impact on long term volatility of market B / Or the situation can long term volatility in market A has a poisitive impact on long term volatility of market B.

Can you explain what is theoritical meaning /interpretation of positive or negative?

The "long-term" volatility is a complicated function of all the GARCH coefficients (the C's, A's and B's)---you can't tell much of anything from a single coefficient in isolation. If you're talking about the conditional volatility; no in a BEKK model the effect of one variance on another is always positive (the coefficients square). It's a fool's errand to try to interpret individual coefficients in a BEKK model.

Dear Tom,

I have a few more questions

1) Why dont we use control variables in BEKK GARCH models? i mean suppose we are studying the spillover from bond markets to stock markets (there is a unanticipated interest rate hike by central bank resulting in volatility in bond markets and also stock markets. Now suppose when we run BEKK GARCH we find significant volatility spillover + shock transmission from bond markets to stock markets. Many times questions are asked why like regression you dont use control variables in BEKK garch to make sure the spillover is really from bond markets to stock markets and not due to other factors

2) Is it advisable to use VAR/VECM models when we are looking at first order mean effect relationship between variables and GARCH models when we are mostly focussing on second order volatility linkages?

Kindly advice