Bayesian estimation of regime-switching GARCH models
Titre du projet
Bayesian estimation of regime-switching GARCH models
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.
Van Dijk, Herman
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- PublicationAccès libreFinancial Risk Management with Bayesian Estimation of GARCH Models: Theory and Applications(Heidelberg: Springer, 2008)This book presents in detail methodologies for the Bayesian estimation of single-regime and regime-switching GARCH models. These models are widespread and essential tools in financial econometrics and have, until recently, mainly been estimated using the classical Maximum Likelihood technique. As this study aims to demonstrate, the Bayesian approach offers an attractive alternative which enables small sample results, robust estimation, model discrimination and probabilistic statements on nonlinear functions of the model parameters. The first two chapters introduce the work and give a short overview of the Bayesian paradigm for inference. The next three chapters describe the estimation of the GARCH model with Normal innovations and the linear regression models with conditionally Normal and Student-t-GJR errors. For these models, we compare the Bayesian and Maximum Likelihood approaches based on real financial data. In particular, we document that even for fairly large data sets, the parameter estimates and confidence intervals are different between the methods. Caution is therefore in order when applying asymptotic justifications for this class of models. The sixth chapter presents some financial applications of the Bayesian estimation of GARCH models. We show how agents facing different risk perspectives can select their optimal VaR point estimate and document that the differences between individuals can be substantial in terms of regulatory capital. Finally, the last chapter proposes the estimation of the Markov-switching GJR model. An empirical application documents the in- and out-of-sample superiority of the regime-switching specification compared to single-regime GJR models. We propose a methodology to depict the density of the one-day ahead VaR and document how specific forecasters’ risk perspectives can lead to different conclusions on the forecasting performance of the MS-GJR model.
- PublicationMétadonnées seulementAdMit: Adaptive mixtures of Student-t distributionsThis short note presents the R package AdMit which provides flexible functions to approximate a certain target distribution and it provides an efficient sample of random draws from it, given only a kernel of the target density function. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. To illustrate the use of the package, we apply the AdMit methodology to a bivariate bimodal distribution. We describe the use of the functions provided by the package and document the ability and relevance of the methodology to reproduce the shape of non-elliptical distributions.
- PublicationMétadonnées seulementAdaptive mixture of Student-t distributions as a flexible distribution for efficient simulation: The R package AdMitThis paper presents the R package AdMit which provides flexible functions to approximate a certain target distribution and to efficiently generate a sample of random draws from it, given only a kernel of the target density function. The core algorithm consists of the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest. Then, importance sampling or the independence chain Metropolis-Hastings algorithm is used to obtain quantities of interest for the target density, using the fitted mixture as the importance or candidate density. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The relevance of the package is shown in two examples. The first aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian estimation of a mixture of ARCH model fitted to foreign exchange log-returns data. The methodology is compared to standard cases of importance sampling and the Metropolis-Hastings algorithm using a naive candidate and with the Griddy-Gibbs approach.
- PublicationMétadonnées seulementBayesian estimation of the GARCH(1,1) model with Student-t innovations in R(2010)
;Hoogerheide, LennartThis paper presents the R package bayesGARCH which provides functions for the Bayesian estimation of the parsimonious but effective GARCH(1,1) model with Student-t innovations. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The usage of the package is shown in an empirical application to exchange rate log-returns.
- PublicationMétadonnées seulementA comparative study of Monte Carlo methods for efficient evaluation of marginal likelihoods(2012)
; ;Basturk, Nalan ;Hoogerheide, LennartVan Dijk, HermanStrategic choices for efficient and accurate evaluation of marginal likelihoods by means of Monte Carlo simulation methods are studied for the case of highly non-elliptical posterior distributions. A comparative analysis is presented of possible advantages and limitations of different simulation techniques; of possible choices of candidate distributions and choices of target or warped target distributions; and finally of numerical standard errors. The importance of a robust and flexible estimation strategy is demonstrated where the complete posterior distribution is explored. Given an appropriately yet quickly tuned adaptive candidate, straightforward importance sampling provides a computationally efficient estimator of the marginal likelihood (and a reliable and easily computed corresponding numerical standard error) in the cases investigated, which include a non-linear regression model and a mixture GARCH model. Warping the posterior density can lead to a further gain in efficiency, but it is more important that the posterior kernel be appropriately wrapped by the candidate distribution than that it is warped.
- PublicationMétadonnées seulementBayesian estimation of a Markov-switching threshold GARCH model with Student-t innovations(2009)A Bayesian estimation of a regime-switching threshold asymmetric GARCH model is proposed. The specification is based on a Markov-switching model with Student-t innovations and K separate GJR(1,1) processes whose asymmetries are located at free non-positive threshold parameters. The model aims at determining whether or not: (i) structural breaks are present within the volatility dynamics; (ii) asymmetries (leverage effects) are present, and are different between regimes and (iii) the threshold parameters (locations of bad news) are similar between regimes. A novel MCMC scheme is proposed which allows for a fully automatic Bayesian estimation of the model. The presence of two distinct volatility regimes is shown in an empirical application to the Swiss Market Index log-returns. The posterior results indicate no differences with regards to the asymmetries and their thresholds when comparing highly volatile periods with the milder ones. Comparisons with a single-regime specification indicates a better in-sample fit and a better forecasting performance for the Markov-switching model.
- PublicationMétadonnées seulementMarkov-switching GARCH models in R: The MSGARCH package(2019)
; ; ;Boudt, Kris ;Catania, LeopoldoTrottier, Denis-Alexandre
- PublicationMétadonnées seulementForecasting risk with Markov-switching GARCH models: A large-scale performance study(2018)
; ; ;Boudt, KrisCatania, Leopoldo
- PublicationMétadonnées seulementRegime changes in Bitcoin GARCH volatility dynamics(2019)
; ;Ruede, Maxime