Bayesian estimation of regime-switching GARCH models
Project responsable | David Ardia |
Project partner |
Lennart Hoogerheide
Herman Van Dijk |
Abstract |
The purpose of this project is to extend the work of my Ph.D. thesis
on the Bayesian estimation of Markovswitching GARCH (MS-GARCH)
models. In particular, I will pursue three extensions of Ardia
(2007). First, a generalization of the MS-GARCH model will be
undertaken by allowing the transition probabilities to change over
time according to some exogenous variables; the approaches proposed
by Filardo and Gordon (1998) and Geweke and Keane (2007) will be
used as starting point for my research. My aim will be to identify
empirically if these exogenous factors influence the triggering
mechanism of the volatility process, and if the impact varies
across regimes. The Bayesian approach is particularly well suited
to estimate this model and should allow to discriminate between the
two specifications for the transition probabilities’ dynamics
through the estimation of the Bayes factors. Second, I will develop
a MS-GARCH-in-mean model by broadening the initial work of Engle et
al. (1987) to account for different regimes in the volatility
process. My approach will permit to test for the presence of a
dynamic risk premium in the data and if the price of risk is
different between the regimes. To my knowledge, this kind of model
has not been proposed yet in the financial literature. The Bayesian
approach offers an attractive estimation technique since it avoids
the estimation difficulties encountered with the maximum likelihood
technique. Moreover, the estimation of the Bayes factors will permit
to determine which functional form (linear or logarithmic) and which
measure of risk (variance or standard deviation) should be retained
when modeling financial returns. Third, I will consider a MS-GARCH
model with an asymmetric threshold specification for the
conditional variance in each regime. This new class of model will
allow to determine whether a leverage effect is present in the
data, at which level it appears, and if the asymmetry is different
between the regimes. For this class of models, the classical
asymptotic distribution theory for the maximum likelihood estimator
is inoperable, because the log-likelihood function is
nondifferentiable. Fortunately, this difficulty disappears when
Bayesian methods are used. Moreover, testing the presence of a
leverage effect at a non-zero level could be achieved through the
estimation of Bayes factors. |
Keywords |
GARCH, bayesian, volatility, Markov-switching |
Project homepage | http://p3.snf.ch/project-121441 |
Type of project | Applied research project |
Research area | Economics |
Method of financing | Swiss National Science Foundation |
Status | Completed |
Start of project | 3-2008 |
End of project | 2-2009 |
Overall budget | 54,000 CHF |
Additional info |
Fellowships for prospective researchers |
Contact | David Ardia |