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Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture. (English) Zbl 1293.91141
Summary: We extend the asymmetric, stochastic, volatility model by modeling the return-volatility distribution nonparametrically. The novelty is modeling this distribution with an infinite mixture of normals, where the mixture unknowns have a Dirichlet process prior. Cumulative Bayes factors show our semiparametric model accurately forecasting market returns. During tranquil markets, expected volatility rises (declines, then rises as the shock increases) when the market shock is negative (positive). This asymmetry is muted when the market is volatile. In other words, when times are good, no news is good news, but during bad times, neither good nor bad news matters with regards to volatility.

91B70 Stochastic models in economics
62G05 Nonparametric estimation
62F15 Bayesian inference
62H30 Classification and discrimination; cluster analysis (statistical aspects)
Full Text: DOI
[1] Asai, M.; McAleer, M., Multivariate stochastic volatility, leverage and news impact surfaces, Econometrics Journal, 12, 292-309, (2009) · Zbl 1231.91483
[2] Basu, S.; Chib, S., Marginal likelihood and Bayes factors for Dirichlet process mixture models, Journal of the American Statistical Association, 98, 461, 224-235, (2003) · Zbl 1047.62023
[3] Bekaert, G.; Wu, G., Asymmetric volatility and risk in equity markets, Review of Financial Studies, 13, 1-42, (2000)
[4] Black, F., 1976. Studies in stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section of the American Statistical Association, pp. 177-181.
[5] Burda, M.; Prokhorov, A., Copula based factorization in Bayesian multivariate mixture models, technical report, (2012), University of Toronto, Department of Economics
[6] Campbell, J. Y.; Hentschel, L., No news is good news: an asymmetric model of changing volatility in stock returns, Journal of Financial Economics, 31, 281-318, (1992)
[7] Carvalho, C. M.; Lopes, H. F.; Polson, N. G.; Taddy, M. A., Particle learning for general mixtures, Bayesian Analysis, 5, 4, 709-740, (2010) · Zbl 1330.62348
[8] Chen, X.; Ghysels, News-good or bad-and its impact on volatility predictions over multiple horizons, Review of Financial Studies, 24, 46-81, (2011)
[9] Chib, S.; Greenberg, E., Understanding the metropolis-Hastings algorithm, The American Statistician, 49, 327-335, (1995)
[10] Chib, S., Greenberg, E., 1998. Analysis of multivariate probit models, 85, 347-361. · Zbl 0938.62020
[11] Chib, S.; Nardari, F.; Shephard, N., Markov chain Monte Carlo methods for stochastic volatility models, Journal of Econometrics, 108, 281-316, (2002) · Zbl 1099.62539
[12] Christie, A. A., The stochastic behavior of common stock variances: value, leverage and interest rate effects, Journal of Financial Economics, 10, 407-432, (1982)
[13] Das, S. R.; Sundaram, R. K., Of smiles and smirks: a term structure perspective, Journal of Financial and Quantitave Analysis, 34, 2, 211-239, (1999)
[14] Delatola, E.-I.; Griffin, J. E., Bayesian nonparametric modelling of the return distribution with stochastic volatilty, Bayesian Analysis, 6, 1-26, (2011)
[15] Delatola, E.-I.; Griffin, J. E., A Bayesian semiparametric model for volatility with a leverage effect, technical report, (2011), University of Kent · Zbl 1366.62195
[16] Dickey, J. D., The weighted likelihood ratio, linear hypotheses on normal location parameters, Annals of Mathematical Statistics, 42, 204-223, (1971) · Zbl 0274.62020
[17] Durham, G. B., SV mixture models with application to S&P 500 index return, Journal of Financial Economics, 85, 822-856, (2007)
[18] Escobar, M. D., Estimating normal means with a Dirichlet process prior, Journal of the American Statistical Association, 89, 425, 268-277, (1994) · Zbl 0791.62039
[19] Escobar, M. D.; West, M., Bayesian density estimation and inference using mixtures, Journal of the American Statistical Association, 90, 430, 577-588, (1995) · Zbl 0826.62021
[20] Ferguson, T., A Bayesian analysis of some nonparametric problems, The Annals of Statistics, 1, 2, 209-230, (1973) · Zbl 0255.62037
[21] Figlewski, S.; Wang, X., Is the “leverage effect” a leverage effect? technical report, (2000), NYU Stern School of Business
[22] French, K. R.; Schwert, G. W.; Stambaugh, R. F., Expected stock returns and volatility, Journal of Financial Economics, 19, 3-29, (1987)
[23] Gelfand, A. E.; Mukhopadhyay, S., On nonparametric Bayesian inference for the distribution of a random sample, The Canadian Journal of Statistics, 23, 4, 411-420, (1995) · Zbl 0858.62028
[24] Geweke, J., Evaluating the accuracy of sampling based approaches to the calculation of posterior moments, (Bernardo; Berger; Dawid; Smith, Bayesian Statistics, Vol. 4, (1992), Clarendon Press Oxford)
[25] Geweke, J., Bayesian econometric and forecasting, Journal of Econometrics, 100, 11-15, (2001) · Zbl 0996.62099
[26] Geweke, J.; Amisano, G., Comparing and evaluating Bayesian predictive distributions of asset returns, International Journal of Forecasting, 26, 216-230, (2010)
[27] Geweke, J.; Whiteman, C., Bayesian forecasting, (Elliot, G.; Granger, C.; Timmermann, A., Handbook of Economic Forecasting, (2006), Elsevier Amsterdam)
[28] Griffin, J. E., Default priors for density estimation with mixture models, Bayesian Analysis, 5, 45-64, (2011) · Zbl 1330.62127
[29] Griffin, J. E.; Steel, M. F.J., Ordered-based dependent Dirichlet processes, Journal of the American Statistical Association, 101, 179-194, (2006) · Zbl 1118.62360
[30] Griffin, J. E.; Steel, M. F.J., Stick-breaking autoregressive processes, Journal of Econometrics, 162, 383-396, (2011) · Zbl 1441.62709
[31] Harvey, A.; Ruiz, E.; Shephard, N., Multivariate stochastic variance models, The Review of Economic Studies, 61, 2, 247-264, (1994) · Zbl 0805.90026
[32] Jacquier, E.; Polson, N. G.; Rossi, P. E., Bayesian analysis of stochastic volatility models, Journal of Business & Economic Statistics, 12, 371-417, (1994)
[33] Jacquier, E.; Polson, N. G.; Rossi, P. E., Bayesian analysis of stochastic volatility models with fat-tails and correlated errors, Journal of Econometrics, 122, 185-212, (2004) · Zbl 1328.91254
[34] Jefferies, H., Theory of probability, (1961), Clarendon Press
[35] Jensen, M. J., Semiparametric Bayesian inference of long-memory stochastic volatility models, Journal of Time Series Analysis, 25, 6, 895-922, (2004) · Zbl 1062.62232
[36] Jensen, M. J.; Maheu, J. M., Bayesian semiparametric stochastic volatility modeling, Journal of Econometrics, 157, 2, 306-316, (2010) · Zbl 1431.62477
[37] Kim, S.; Shephard, N.; Chib, S., Stochastic volatility: likelihood inference and comparison with arch models, Review of Economic Studies, 65, 361-393, (1998) · Zbl 0910.90067
[38] Lo, A. Y., On a class of Bayesian nonparametric estimates, I. density estimates, The Annals of Statistics, 12, 351-357, (1984) · Zbl 0557.62036
[39] MacEachern, S. N.; Müller, P., Estimating mixture of Dirichlet process models, Journal of Computational and Graphical Statistics, 7, 2, 223-238, (1998)
[40] Nelson, D. B., Conditional heteroskedasticity in asset returns: a new approach, Econometrica, 59, 347-370, (1991) · Zbl 0722.62069
[41] Omori, Y.; Chib, S.; Shephard, N.; Nakajima, J., Stochastic volatility with leverage: fast and efficient likelihood inference, Journal of Econometrics, 140, 2, 425-449, (2007) · Zbl 1247.91207
[42] Percival, D. B.; Walden, A. T., Spectral analysis for physical applications: multitaper and conventional univariate techniques, (1993), Cambridge University Press · Zbl 0796.62077
[43] Poon, S.; Granger, C. W., Forecasting volatility in financial markets: a review, Journal of Economic Literature, 41, 478-539, (2003)
[44] Rey, M.; Roth, V., Copula mixture model for dependency-seeking clustering, technical report. proceeding of the 29th international conference on machine learning, (2012)
[45] Schwert, G., Why does stock market volatility change over time?, Journal of Finance, 44, 1115-1154, (1989)
[46] Sethuraman, J., A constructive definition of Dirichlet priors, Statistica Sinica, 4, 639-650, (1994) · Zbl 0823.62007
[47] West, M.; Muller, P.; Escobar, M., Hierarchical priors and mixture models with applications in regression and density estimation, (Freeman, P. R.; Smith, A. F., Aspects of Uncertainty, (1994), John Wiley) · Zbl 0842.62001
[48] Yu, J., On leverage in a stochastic volatility model, Journal of Econometrics, 127, 2, 165-178, (2005) · Zbl 1335.91116
[49] Yu, J., A semiparametric stochastic volatility model, Journal of Econometrics, 176, 473-482, (2011) · Zbl 1441.62909
[50] Zellner, A., An introduction to Bayesian inference in econometrics, (1971), Wiley New York · Zbl 0246.62098
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