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.

[1]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[2]  S. Frühwirth-Schnatter,et al.  Analysis of Exchange Rates via Multivariate Bayesian Factor Stochastic Volatility Models , 2014 .

[3]  J. Geweke,et al.  Comparing and Evaluating Bayesian Predictive Distributions of Asset Returns , 2008 .

[4]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[5]  H. Jeffreys,et al.  The Theory of Probability , 1896 .

[6]  H. Rue.  Fast sampling of Gaussian Markov random fields , 2000 .

[7]  N. Shephard,et al.  Stochastic volatility with leverage: Fast and efficient likelihood inference , 2007 .

[8]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[9]  C. D. Litton,et al.  Theory of Probability (3rd Edition) , 1984 .

[10]  Gregor Kastner,et al.  Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models , 2014, Comput. Stat. Data Anal..

[11]  Tim Bollerslev,et al.  Glossary to ARCH (GARCH) , 2008 .

[12]  Torben G. Andersen,et al.  Stochastic volatility , 2003 .

[13]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[14]  S. Taylor.  Financial Returns Modelled by the Product of Two Stochastic Processes , 1961 .

[15]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[16]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[17]  William J. McCausland,et al.  Simulation smoothing for state-space models: A computational efficiency analysis , 2011, Comput. Stat. Data Anal..

[18]  Francesca Ieva,et al.  The contribution of young researchers to Bayesian statistics : proceedings of BAYSM2013 , 2014 .

[19]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[20]  Peter E. Rossi,et al.  Bayesian analysis of stochastic volatility models with fat-tails and correlated errors , 2004 .

[21]  Charles S. Bos.  Relating Stochastic Volatility Estimation Methods , 2011 .

[22]  M. Plummer,et al.  CODA: convergence diagnosis and output analysis for MCMC , 2006 .

[23]  Jun Yu.  On Leverage in a Stochastic Volatility Model , 2004 .

[24]  Siddhartha Chib,et al.  Stochastic Volatility with Leverage: Fast Likelihood Inference , 2004 .

[25]  Dirk Eddelbuettel,et al.  Rcpp: Seamless R and C++ Integration , 2011 .

[26]  S. Frühwirth-Schnatter,et al.  Stochastic model specification search for Gaussian and partial non-Gaussian state space models , 2010 .

[27]  Yaming Yu,et al.  To Center or Not to Center: That Is Not the Question—An Ancillarity–Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency , 2011 .

[28]  Jun Yu,et al.  Bugs for a Bayesian Analysis of Stochastic Volatility Models , 2000 .

[29]  Gregor Kastner.  Efficient Bayesian Inference for Stochastic Volatility (SV)Models , 2016 .