Bayesian modeling of financial returns: A relationship between volatility and trading volume

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  T. Andersen.  Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility , 1996 .

[2]  Christopher G. Lamoureux,et al.  Persistence in Variance, Structural Change, and the GARCH Model , 1990 .

[3]  Raul Susmel,et al.  Regime-Switching Stochastic Volatility and Short-Term Interest Rates , 2001 .

[4]  F. Foster,et al.  Can Speculative Trading Explain the Volume–Volatility Relation? , 1995 .

[5]  Peter C. Schotman,et al.  An empirical application of stochastic volatility models , 1998 .

[6]  M. Richardson,et al.  A Direct Test of the Mixture of Distributions Hypothesis: Measuring the Daily Flow of Information , 1994, Journal of Financial and Quantitative Analysis.

[7]  P. Clark.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices , 1973 .

[8]  Toshiaki Watanabe,et al.  Block sampler and posterior mode estimation for asymmetric stochastic volatility models , 2007, Comput. Stat. Data Anal..

[9]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[10]  James D. Hamilton.  Analysis of time series subject to changes in regime , 1990 .

[11]  Benoit B. Mandelbrot,et al.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices: Comment , 1973 .

[12]  N. Shephard,et al.  Markov chain Monte Carlo methods for stochastic volatility models , 2002 .

[13]  Philip Heidelberger,et al.  Simulation Run Length Control in the Presence of an Initial Transient , 1983, Oper. Res..

[14]  Toshiaki Watanabe.  Bayesian Analysis of Dynamic Bivariate Mixture Models: Can They Explain the Behavior of Returns and Trading Volume? , 2000 .

[15]  N. Shephard,et al.  The simulation smoother for time series models , 1995 .

[16]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[17]  Yasuhiro Omori,et al.  Multi-move sampler for estimating non-Gaussian time series models: Comments on Shephard and Pitt (1997) , 2001 .

[18]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[19]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[20]  T. Andersen.  Stochastic Autoregressive Volatility: A Framework for Volatility Modeling , 1994 .

[21]  Lawrence Harris,et al.  Transaction Data Tests of the Mixture of Distributions Hypothesis , 1987, Journal of Financial and Quantitative Analysis.

[22]  Carlos M. Carvalho,et al.  Simulation-based sequential analysis of Markov switching stochastic volatility models , 2007, Comput. Stat. Data Anal..

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

[24]  Mike K. P. So,et al.  A Stochastic Volatility Model With Markov Switching , 1998 .

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

[26]  M. Pitt,et al.  Likelihood analysis of non-Gaussian measurement time series , 1997 .

[27]  Jun Yu,et al.  Deviance Information Criterion for Comparing Stochastic Volatility Models , 2002 .

[28]  Jonathan M. Karpoff.  The Relation between Price Changes and Trading Volume: A Survey , 1987, Journal of Financial and Quantitative Analysis.

[29]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[30]  Daniel Pemstein,et al.  The Scythe Statistical Library: An Open Source C++ Library for Statistical Computation , 2011 .

[31]  Paul R. Milgrom,et al.  Bid, ask and transaction prices in a specialist market with heterogeneously informed traders , 1985 .

[32]  Roman Liesenfeld,et al.  Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions , 1997 .

[33]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[34]  C. Robert,et al.  Deviance information criteria for missing data models , 2006 .

[35]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[36]  Toshiaki Watanabe,et al.  Bayesian Analysis of a Markov Switching Stochastic Volatility Model , 2005 .

[37]  S. Koopman,et al.  Disturbance smoother for state space models , 1993 .

[38]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[39]  George Tauchen,et al.  THE PRICE VARIABILITY-VOLUME RELATIONSHIP ON SPECULATIVE MARKETS , 1983 .

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

[41]  Toshiaki Watanabe,et al.  A multi‐move sampler for estimating non‐Gaussian time series models: Comments on Shephard & Pitt (1997) , 2004 .

[42]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[43]  James D. Hamilton.  Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates , 1988 .