Approaches Toward the Bayesian Estimation of the Stochastic Volatility Model with Leverage

The sampling efficiency of MCMC methods in Bayesian inference for stochastic volatility (SV) models is known to highly depend on the actual parameter values, and the effectiveness of samplers based on different parameterizations varies significantly. We derive novel algorithms for the centered and the non-centered parameterizations of the practically highly relevant SV model with leverage, where the return process and innovations of the volatility process are allowed to correlate. Moreover, based on the idea of ancillarity-sufficiency interweaving (ASIS), we combine the resulting samplers in order to guarantee stable sampling efficiency irrespective of the baseline parameterization.We carry out an extensive comparison to already existing sampling methods for this model using simulated as well as real world data

Sparse Bayesian vector autoregressions in huge dimensions

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions. This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities

EUROPEAN RAPESEED AND FOSSIL DIESEL: THRESHOLD COINTEGRATION ANALYSIS AND POSSIBLE IMPLICATIONS

For European operators of biofuels plants there are not many hedge vehicles available to hedge operational margins. Cross hedges for rapeoil (with the rapeseed futures contract) and RME (with the NYMEX diesel futures contract) could be useful instruments. We use recent developments on threshold cointegration approaches to investigate if asymmetric dynamic adjusting processes exist among rapeseed and diesel prices. The results suggest that a threeregime threshold cointegration model suitably explains the dynamics of the data.Hedging, Rapeseed, Heating Oil, Threshold cointegration analysis, Agribusiness, Agricultural and Food Policy, Agricultural Finance, Crop Production/Industries, Demand and Price Analysis, Environmental Economics and Policy, Farm Management, Financial Economics, Industrial Organization, Institutional and Behavioral Economics, Production Economics,

Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models

Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving has recently been shown to aid in overcoming these issues for a broad class of multilevel models. In this paper, we demonstrate how such an interweaving strategy can be applied to stochastic volatility models in order to greatly improve sampling efficiency for all parameters and throughout the entire parameter range. Moreover, this method of "combining best of different worlds" allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand.Series: Research Report Series / Department of Statistics and Mathematic

Investigating the Dark Figure of COVID-19 Cases in Austria: Borrowing From the Decode Genetics Study in Iceland

The number of undetected cases of SARS-CoV-2 infections is expected to be a multiple of the reported figures mainly due to the assumed high proportion of asymptomatic infections and to limited availability of trustworthy testing resources. Relying on the deCODE genetics study in Iceland, which offers large scale testing among the general population, we investigate the magnitude and uncertainty of the number of undetected cases COVID-19 cases in Austria. We formulate several scenarios relying on data on the number of COVID-19 cases which have been hospitalized, in intensive care, as well as on the number of deaths and positive tests in Iceland and Austria. We employ frequentist and Bayesian methods for estimating the dark figure in Austria based on the hypothesized scenarios and for accounting for the uncertainty surrounding this figure. Using data available on April 01, 2020, our study contains two main findings: First, we find the estimated number of infections to be on average around 8.35 times higher than the recorded number of infections. Second, the width of the uncertainty bounds associated with this figure depends highly on the statistical method employed. At a 95% level, lower bounds range from 3.96 to 6.83 and upper bounds range from 9.82 to 12.61. Overall, our findings confirm the need for systematic tests in the general population of Austria

Heavy-Tailed Innovations in the R Package stochvol

We document how sampling from a conditional Student's t distribution is implemented in stochvol. Moreover, a simple example using EUR/CHF exchange rates illustrates how to use the augmented sampler. We conclude with results and implications. (author's abstract

Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?

We assess the relationship between model size and complexity in the time-varying parameter VAR framework via thorough predictive exercises for the Euro Area, the United Kingdom and the United States. It turns out that sophisticated dynamics through drifting coefficients are important in small data sets while simpler models tend to perform better in sizeable data sets. To combine best of both worlds, novel shrinkage priors help to mitigate the curse of dimensionality, resulting in competitive forecasts for all scenarios considered. Furthermore, we discuss dynamic model selection to improve upon the best performing individual model for each point in time

Efficient Bayesian Interference for Stochastic Volatility

Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving (Yu and Meng, 2011) has recently been shown to aid in overcoming these issues for a broad class of multilevel models. This package provides software for "combining best of different worlds" which allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand

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. (author's abstract