structural breaks in conditional variance equation

[irfanawan]

Dear Tom,
I wants to include variance breaks in conditional variance equations of Multivariate GARCH models.
Suppose that I have two returns series i.e. R1 and R2. My procedure detect two breaks in variance of R1 and and three in variance of R2.
Now how can I introduce two dummies in conditional variance equation of R1 and three dummies in conditional variance equation of R2. This was done by Mensi at el. (2015) in their paper entitled " Structural breaks, dynamic correlation, asymmetric volatility transmission, and hedging strategies for petroleum prices and USD exchange rage" publish in Energy Economics.

[TomDoan]

Dear Tom,
I wants to include variance breaks in conditional variance equations of Multivariate GARCH models.
Suppose that I have two returns series i.e. R1 and R2. My procedure detect two breaks in variance of R1 and and three in variance of R2.
Now how can I introduce two dummies in conditional variance equation of R1 and three dummies in conditional variance equation of R2. This was done by Mensi at el. (2015) in their paper entitled " Structural breaks, dynamic correlation, asymmetric volatility transmission, and hedging strategies for petroleum prices and USD exchange rage" publish in Energy Economics.

Note that they're using a non-standard definition of DCC---to most people DCC now has a specific meaning, and it's not their equations (6) and (7). They are using the Koutmos model for the spillover effects in the EGARCH. That would have to be done using MAXIMIZE (since it's non-standard both in the form of DCC and in the use of differing variance shifts between the two series in each pair), and would best be based upon the Koutmos JBFA 1996 program.

[mengqi]

Dear Tom,

How can I include variance structural breaks in conditional variance-covariance equations for BEKK model?

Kind regards

[TomDoan]

XREGRESSORS with dummies for the structural breaks.

[emna]

Dear irfanawan,
I want to estimate the same model. how can i did it please ?
Thank you

[TomDoan]

Dear irfanawan,
I want to estimate the same model. how can i did it please ?
Thank you

There are several things about the Mensi et al (2015) paper that are statistically questionable.

1. If the DGP is a (fairly persistent) GARCH model, the ICSS procedure can "detect" several variance regimes. If the DGP is actually a set of episodes of different variances (what ICSS is actually designed to look for), then a GARCH "model" will often fit reasonably well, usually with fairly persistent GARCH coefficients. Combining the GARCH with ICSS-determined breaks is probably the worst of all possible worlds.
2. Tests of the significance of the dummies in the dummied-segment GARCH model will have (probably a very) non-standard distribution since the dummies are chosen using a pre-test calculation.
3. Probably most important, structural breaks are a property of a model, not of a series. Their procedure is to look at univariate analyses of the variances, then to put those separately identified dummies into a bivariate model. However, the bivariate model allows for spillovers in the variances. The dummies, on the other hand, are unmodelled variance shifts. How can you tell if there is variance spillover from x to y if you already have a dummy in the model that says that y has a high variance during period ... due to reasons having nothing to do with x? (Answer: you can't).

[jackzhai1989]

Dear Tom,

I am sorry but I am quite new to VAR-BEKK-GARCH model and I just started using Rats. Similar to irfanawan, I also detect two breaks in variance of R1 and and three in variance of R2. So how could I introduce the detected structural breaks indicated by dummy variables into each variance equations for BEKK model separately? I use the xerg option and include a supplementary card listing the dummies which is recommended by the user's guide but I find that the same shifts are applied to all variance equations in the results (as shown in the attachment 20180411.rpf). What I want to do is add two dummies in conditional variance equation of R1 and three dummies in conditional variance equation of R2 just like the work of Ewing and Malik (2005) in JBF. Could you please help me to handle this problem？ Thank you !

Sincerely，
Jack Zhai

[TomDoan]

All three points in https://estima.com/forum/viewtopic.php?p=15075#p15075 apply to that, and, in addition, the way they incorporate the dummies into the BEKK is just plain wrong. Note that each of those final terms is (by construction) positive definite, which means that it can only increase variance. What happens if a "variance break" reduces the variance. This can't handle that. Plus they put the "first" break dummy for each of the series into the same D term, then do the same with the second, and third, even though those are separately identified. There's no good reason to lump break point 1 from series 1 with break point 1 from series 2.

While this was done with RATS, it was a RATS before the GARCH instruction, so they wouldn't have been able to use GARCH with XREG. However, XREG applied to a BEKK, by default handles the dummies differently than this (for the reason just mentioned). See the description of the XBEKK option on https://estima.com/ratshelp/garchinstruction.html. (How they handle the dummies isn't either option for that, I really don't understand the point of slamming unrelated dummies into the same matrix calculation).

This whole concept (pre-testing individual series, then adding dummies to a GARCH based upon them) is just a bad idea.

[jackzhai1989]

Thank you very much for your response, Tom! It is a great support and help!