74th International Atlantic Economic Conference

October 04 - 07, 2012 | Montréal, Canada

Discriminating between GARCH and stochastic volatility via nonnested hypotheses testing

Friday, October 5, 2012: 9:20 AM
Philip Messow, M.Sc. , Statistics, Dortmund University, Dortmund, Germany
Modeling conditional volatility is among the most important tasks of financial
econometrics Two competing models, with a different economic interpretation,
are the main workhorses in this field. The GARCH-model, where
the conditional volatility is described by past observations and the class of
SV-models, where additional uncertainty enters via some extra error term.
While GARCH-models are much easier to estimate, SV-models provide less
restrictions on conditional moments than GARCH-models (Meddahi and Renault,
2004). From a practitioner’s point of view it would be interesting to
know if the estimation of the much more difficult SV-model is worth the effort.
Furthermore, GARCH- and SV-models yield different economic interpretations.
Due to the extra error term within the framework of the SV-model, the
conditional variance process is a function of latent variables, which can be
interpreted as the random and uneven flow of information (e.g. volume of transactions or the order book).
The GARCH-model in lieu thereof assumes that the conditional variance is
perfectly explained by past observations. This economic aspect as well as
the practical handling raises interest in discriminating between both of these
Tests to decide whether a GARCH- or a SV-model is appropriate go back to
Kim et al. (1998) and normally rely on nested hypothesis testing. Popular
examples are Kobayashi and Shi (2005) and Franses et al. (2008). One major
disadvantage of this type of model selection technique is that these tests
implicitly assume that one of the models is the true data generating process
(DGP). But, as pointed out by Hansen (2005), models used by econometricians
are just approximations to the true DGP. The goal of a model selection
technique should be to find a good approximation of the true DGP. That
would include that neither the specific (nested) GARCH- nor the specific
SV-model is a good approximation to the true DGP. In this paper we circumvent
this problem by applying the popular J-test of Davidson and MacKinnon
(1981) to the problem of discriminating between GARCH- and SV-models.
By using this method it is possible that both models are rejected, none of
these models are rejected or just one model is rejected. Because the proposed
test experiences serious lack of power for finite samples (Davidson and
MacKinnon, 2002), we use a bootstrapped version of the test and compare
the finite sample properties of the test and its bootstrapped counterpart.
We employ the proposed test to find out whether stock index returns (e.g.
DAX, Euro Stoxx 50) and exchange rates (e.g. EUR/USD) are better modeled
by GARCH- or SV-models.

Davidson, R., MacKinnon, J.G., 1981. Several tests for model specification
in the presence of alternative hypotheses. Econometrica 49, 781–793.
Davidson, R., MacKinnon, J.G., 2002. Bootstrap J tests of nonnested linear
regression models. Journal of Econometrics 109, 167–193.
Franses, P.H., van der Leij, M., Paap, R., 2008. A simple test for GARCH
against a stochastic volatility model. Journal of Financial Econometrics 6,
Hansen, B.E., 2005. Challenges for econometric model selection. Econometric
Theory 21, 60–68.
Kim, S., Shepard, N., Chib, S., 1998. Stochastic volatility: Likelihood inference
and comparison with ARCH models. Review of Economic Studies 65,
Kobayashi, M., Shi, X., 2005. Testing for EGARCH against stochastic volatility
models. Journal of Time Series Analysis 26, 135–150.
Meddahi, N., Renault, E., 2004. Temporal aggregation of volatility models.
Journal of Econometrics 119, 355–379.