Gregor Kastner

Dealing with Stochastic Volatility in Time Series Using the R Package stochvol

The R package stochvol provides a fully Bayesian implementation of heteroskedasticity modeling within the framework of stochastic volatility. It utilizes Markov chain Monte Carlo (MCMC) samplers to conduct inference by obtaining draws from the posterior distribution of parameters and latent variables which can then be used for predicting future volatilities. The package can straightforwardly be employed as a stand-alone tool; moreover, it allows for easy incorporation into other MCMC samplers. The main focus of this paper is to show the functionality of stochvol. In addition, it provides a brief mathematical description of the model, an overview of the sampling schemes used, and several illustrative examples using exchange rate data.

Analysis of Exchange Rates via Multivariate Bayesian Factor Stochastic Volatility Models

Multivariate factor stochastic volatility (SV) models are increasingly used for the analysis of multivariate financial and economic time series because they can capture the volatility dynamics by a small number of latent factors. The main advantage of such a model is its parsimony, as the variances and covariances of a time series vector are governed by a low-dimensional common factor with the components following independent SV models. For high-dimensional problems of this kind, Bayesian MCMC estimation is a very efficient estimation method; however, it is associated with a considerable computational burden when the dimensionality of the data is moderate to large. To overcome this, we avoid the usual forward-filtering backward-sampling (FFBS) algorithm by sampling “all without a loop” (AWOL), consider various reparameterizations such as (partial) noncentering, and apply an ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation at a univariate level, which can be applied directly to heteroskedasticity estimation for latent variables such as factors. To show the effectiveness of our approach, we apply the model to a vector of daily exchange rate data.

Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models

ABSTRACT We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies to substantially accelerate convergence and mixing of standard MCMC approaches. Similar to marginal data augmentation techniques, the proposed acceleration procedures exploit nonidentifiability issues which frequently arise in factor models. Our new interweaving strategies are easy to implement and come at almost no extra computational cost; nevertheless, they can boost estimation efficiency by several orders of magnitude as is shown in extensive simulation studies. To conclude, the application of our algorithm to a 26-dimensional exchange rate dataset illustrates the superior performance of the new approach for real-world data. Supplementary materials for this article are available online.

Bayesian Statistics from Methods to Models and Applications

Bayesian nonparametric marginal methods are very popular since they lead to fairly easy implementation due to the formal marginalization of the infinitedimensional parameter of the model. However, the straightforwardness of these methods also entails some limitations: they typically yield point estimates in the form of posterior expectations, but cannot be used to estimate non-linear functionals of the posterior distribution, such as median, mode or credible intervals. This is particularly relevant in survival analysis where non-linear functionals such as e.g. the median survival time, play a central role for clinicians and practitioners. The main goal of this paper is to summarize the methodology introduced in Arbel et al (2015) for hazard mixture models in order to draw approximate Bayesian inference on survival functions that is not limited to the posterior mean. In addition, we propose a practical implementation of an R package called momentify designed for moment-based density approximation, and, by means of an extensive simulation study, we thoroughly compare the introduced methodology with standard marginal methods and empirical estimation.