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Bayesian modeling of financial returns: a relationship between volatility and trading volume. (English) Zbl 1224.91179
This paper investigates the joint distribution of daily returns and trading volume based on the modified mixture model with Markov switching volatility specification. The authors extend this specification to heavier-tailed distributions for the returns using an algorithm based on Markov Chain Monte Carlo simulation methods is constructed to estimate all parameters and latent quantities in the model using the Bayesian approach. The authors are able to produce an estimate of the latent information process, which can be used in financial modeling. The obtained estimation result shows that the estimate of the persistence parameters drops and the estimate of the variance error rises in the volatility specification. Markov switching models are supported by the British Petroleum data.

91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
91G70 Statistical methods; risk measures
Full Text: DOI
[1] Karpoff, The relation between price changes and trading volume: a survey, The Journal of Financial and Quantitative Analysis 22 pp 109– (1987)
[2] Clark, A subordinated stochastic process model with finite variance for speculative prices, Econometrica 41 pp 135– (1973) · Zbl 0308.90011
[3] Tauchen, The price variability-volume relationships in speculative markets, Econometrica 51 pp 485– (1983) · Zbl 0495.90026
[4] Richardson, A direct test of the mixture distribution hypothesis: measuring the daily flow of information, The Journal of Financial and Quantitative Analysis 15 pp 183– (1994)
[5] Foster, Can speculative trading explain the trading volume relation, Journal of Business and Economic Statistics 13 pp 379– (1995)
[6] Harris, Transaction data test of the mixture distribution hypothesis, The Journal of Financial and Quantitative Analysis 22 pp 127– (1987)
[7] Andersen, Return volatility and trading volume: an information flow interpretation of stochastic volatility, Journal of Finance 51 pp 169– (1996)
[8] Andersen, Stochastic autoregressive volatility: a framework for volatility modeling, Mathematical Finance 4 pp 75– (1994) · Zbl 0884.90013
[9] Mahieu, A Bayesian analysis of stock return volatility and trading volume, Applied Financial Economics 8 pp 671– (1998)
[10] Watanabe, Bayesian analysis of dynamic bivariate mixture models: can they explain the behavior of returns and trading volume?, Journal of Business and Economic Statistics 18 pp 199– (2000)
[11] Lamoureux, Persistence in variance, structural change, and the GARCH, Journal of Business and Economic Statistics 8 pp 225– (1998)
[12] Hamilton, Autoregressive conditional heteroskedasticity and changes in regime, Journal of Econometrics 45 pp 39– (1994) · Zbl 0825.62950
[13] So, A stochastic volatility model with Markov switching, Journal of Business and Economic Statistics 15 pp 183– (1998)
[14] Kalimipalli, Regime-switching stochastic volatility and short-term interest rates, Journal of Empirical Finance 11 pp 309– (2004)
[15] Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57 pp 357– (1989) · Zbl 0685.62092
[16] Glosten, Bid, ask, and transaction prices in a specialist market with heterogeneously informed traders, Journal of Financial Economics 14 pp 71– (1985)
[17] Jacquier, Bayesian analysis of stochastic volatility models, Journal of Business and Economic Statistics 12 pp 371– (1994)
[18] Kim, Stochastic volatility: likelihood inference and comparison with ARCH models, Review of Economic Studies 65 pp 361– (1998) · Zbl 0910.90067
[19] Mahieu, An empirical application of stochastic volatility models, Journal of Applied Econometrics 13 pp 333– (1998)
[20] Abanto-Valle CA, Lopes HF, Migon HS. Stochastic volatility estimation: a modern dynamic model viewpoint. Technical Report 210, Departament of Statistics, Federal University of Rio de Janeiro, 2007.
[21] Liesenfeld, Stochastic volatility models: conditional normality versus heavy-tailed distrutions, Journal of Applied Econometrics 15 pp 137– (2000)
[22] Chib, Markov chain Monte Carlo methods for stochastic volatility models, Journal of Econometrics 108 pp 281– (2002) · Zbl 1099.62539
[23] Jacquier, Bayesian analysis of stochastic volatility models with Fat-tails and correlated errors, Journal of Econometrics 122 pp 185– (2004) · Zbl 1328.91254
[24] Shibata, Bayesian analysis of a Markov switching stochastic volatility model, Journal of the Japan Statistical Society 35 pp 205– (2005) · doi:10.14490/jjss.35.205
[25] Shephard, Likelihood analysis of non-Gaussian measurements time series, Biometrika 84 pp 653– (1997) · Zbl 0888.62095
[26] Watanabe, A multi-move sampler for estimate non-Gaussian time series model: comments on Shepard and Pitt (1997), Bimetrika 91 pp 246– (2004)
[27] Omori, Block sampler and posterior mode estimation for asymmetric stochastic volatility models, Computational Statistics and Data Analysis 52 pp 2892– (2008) · Zbl 05564678
[28] Tierney, Markov chains for exploring posterior distributions (with discussion), Annal of Statistics 21 pp 1701– (1994) · Zbl 0829.62080
[29] Chib, Understanding the Metropolis-Hastings algorithm, The American Statistician 49 pp 327– (1995)
[30] de Jong, The simulation smoother for time series models, Biometrika 82 pp 339– (1995) · Zbl 0823.62072
[31] Koopman, Disturbance smoothers for state space models, Biometrika 80 pp 117– (1993) · Zbl 0769.62069
[32] Pemstein, The Scythe statistical library: an open source C++ library for statistical computation, Journal of Statistical Software V pp 1– (2007)
[33] Geweke, Bayesian Statistics 4 pp 169– (1992) · Zbl 1093.62107
[34] Heidelbelger, Simulation run length control in the presence of a initial transient, Operations Research 31 pp 1109– (1983)
[35] Carvalho, Simulation-based sequential analysis of Markov switching stochastic volatility models, Computational Statistics and Data Analysis 51 pp 4526– (2007) · Zbl 1162.62426
[36] Hamilton, Rational expectations econometrics analysis of changes in regime, Journal of Economic Dynamics and Control 12 pp 385– (1988)
[37] Spiegelhalter, Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society, Series B 64 pp 583– (2002) · Zbl 1067.62010
[38] Berg, Deviance information criterion for comparing stochastic volatility models, Journal of Business and Economic Statistics 22 pp 107– (2004)
[39] Celeux, Deviance information criteria for missing data models, Bayesian Analysis 1 pp 651– (2006) · Zbl 1331.62329
[40] Abramowitz, Handbook of Mathematical Functions (1970)
[41] Carter, On Gibbs sampling for state space models, Biometrika 81 pp 541– (1994) · Zbl 0809.62087
[42] Ripley, Stochastic Simulation (1987)
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