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