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A few months ago I've read somewhere that although the exponential GARCH model may lead to higher BIC values in comparison to other extensions of the GARCH family (GARCH, GJR-GARCH, TGARCH, ...), volatility forecasting under this model may lead to biased results. I'm trying to find a trustworthy source (an academic paper) which could back this, but so far I've found

  • this Matlab page which indirectly tells me that results are biased,
  • this 2010 working paper which hasn't been published in any journal, and
  • some bachelor/master theses that report this info without backing it with an academic source.

And as you may imagine, I can't (or better, I don't want to) quote other students' theses in my own thesis.

Do you know of any published work which proves this claim? Or a reliable source which suggests why the EGARCH shouldn't be used for forecasting?

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  • $\begingroup$ In general, higher BIC values indicate inferior models. I think EGARCH has some poor properties; you could check the papers about log-GARCH models by Genaro Sucarrat, I think he contrasts log-GARCH with EGARCH and mentions what's wrong with EGARCH. Here and here you may find just a small remark that proving properties of QML estimator for EGARCH models is difficult and has not been done except for the most basic case. $\endgroup$ – Richard Hardy Aug 8 '16 at 19:09
  • $\begingroup$ Yeah sorry for that, I meant higher BIC values in absolute terms (being negative, of course I meant lower values). But thanks for the links here and in your answer below, I'll check them out! $\endgroup$ – Kondo Aug 8 '16 at 19:35
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I found a couple of papers mentioning bias of EGARCH:

  • Demos, Antonis, and Dimitra Kyriakopoulou. "Bias correction of ML and QML estimators in the EGARCH (1, 1) model." Preprint (2010).
  • Deb, Partha. "Finite sample properties of maximum likelihood and quasi-maximum likelihood estimators of EGARCH models." Econometric Reviews 15.1 (1996): 51-68.

The first one is the same as you mention, so it is of no extra use to you. Probably the second one could be more useful. Unfortunately, I do not have access to it, so I cannot see what is inside.

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This does nor address your question directly, but is somehow related

"We find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns."

Peter R. Hansen, Asger Lunde, A forecast comparison of volatility models: does anything beat a GARCH(1,1)? JAE, Volume 20, Issue 7, December 2005, Pages 873–889

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