On marginal likelihood computation in change-point models

Change-point models are useful for modeling time series subject to structural breaks. For interpretation and forecasting, it is essential to estimate correctly the number of change points in this class of models. In Bayesian inference, the number of change points is typically chosen by the marginal likelihood criterion, computed by Chib's method. This method requires to select a value in the parameter space at which the computation is done. We explain in detail how to perform Bayesian inference for a change-point dynamic regression model and how to compute its marginal likelihood. Motivated by our results from three empirical illustrations, a simulation study shows that Chib's method is robust with respect to the choice of the parameter value used in the computations, among posterior mean, mode and quartiles. Furthermore, the performance of the Bayesian information criterion, which is based on maximum likelihood estimates, in selecting the correct model is comparable to that of the marginal likelihood.BIC, change-point model, Chib's method, marginal likelihood

Bayesian inference for the mixed conditional heteroskedasticity model

We estimate by Bayesian inference the mixed conditional heteroskedasticity model of (Haas, Mittnik, and Paolella 2004a). We construct a Gibbs sampler algorithm to compute posterior and predictive densities. The number of mixture components is selected by the marginal likelihood criterion. We apply the model to the SP500 daily returns.Finite mixture, ML estimation, bayesian inference, value at risk.

On Marginal Likelihood Computation in Change-point Models

Change-point models are useful for modeling times series subject to structural breaks. For interpretation and forecasting, it is essential to estimate correctly the number of change points in this class of models. In Bayesian inference, the number of change-points is typically chosen by the marginal likelihood criterion, computed by Chib’s method. This method requires to select a value in the parameter space at which the computation is done. We explain in detail how to perform Bayesian inference for a change point dynamic regression model and how to compute its marginal likelihood. Motivated by our results from three empirical illustrations, a simulation study shows that Chib’s method is robust with respect to the choice of the parameter value used in the computations, among posterior mean, mode and quartiles. Furthermore, the performance of the Bayesian information criterion, which is based on maximum likelihood estimates, in selecting the correct model is comparable to that of the marginal likelihood.BIC, Change-point model, Chib's method, Marginal likelihood

Theory and inference for a Markov switching GARCH model

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existene of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns.GARCH, Markov-switching, Bayesian inference

Regime switching GARCH models

We develop univariate regime-switching GARCH (RS-GARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specified as a function of past information. We provide sufficient conditions for stationarity and existence of moments. Because of path dependence, maximum likehood estimation is infeasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We apply this model using the NASDAQ daily returns series.GARCH; regime switching; Bayesian inference

Theory and inference for a Markov switching Garch model.

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns.GARCH, Markov-switching, Bayesian inference.

Theory and inference for a Markov switching GARCH model

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns.GARCH, Markov-switching, Bayesian inference

Theory and Inference for a Markov-Switching GARCH Model

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns.GARCH, Markov-switching, Bayesian inference