GARCH ZOO

The large number of models in the GARCH family tend to give one the feeling of wading in to a swamp. Confronted with so many alternatives, the modeler cannot help but wonder how to make a reasonable choice. Except when one follows a specific branch of this family, the models are non-nested, so the traditional information criteria are not helpful. Eventually, one needs to say how one expects to use the chosen model. Once this is done, then it becomes possible to judge the models in terms of their "fitness for use."

Since GARCH family models address the notion of volatility, it is reasonable to consider how well individual models do at forecasting out-of-sample volatility. The paper

Hansen, P. R. and Lunde, A. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)." Journal of Applied Econometrics, March 2004.

take up this idea and the authors --- bless their hearts --- test 330 alternative models. In class we will discuss their list of models (beginning on page 31) and the tables of relative performance that follow in the appendix.

What did they learn?

1. Despite the fact that GARCH(1,1) has a symmetric News Impact Curve and cannot capture any of the so-called leverage effect, GARCH(1,1) could not be proved to be inferior to any later descendents in the GARCH family.
2. This happens even though when one tests the parameters that accommodate the leverage effect, one typically finds parameters that are statistically significant.
3. In this study, high frequency intra day returns were used to measure the observed out-of-sample volatility.
4. There is a certain methodological complexity to the paper, but they covered a great many bases.
5. Things to notice: (a) ARCH is truly horrible, yet it started the whole business (b) Models that do well on the exchange rate data can fail brutally on the stock return data, and vice-versa (c) the measured quality of prediction depends more than one might like on the chosen measurement (d) after ARCH the IGARCH models are particularly terrible.

What's the bottom line?

Volatility prediction is not necessarily the only purpose for a model for the GARCH family, but it certainly in a natural and important use. For example, we should be encouraged to explore GARCH(1,1) more thoroughly in Kelly contexts.