Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models. (English) Zbl 06983987

Summary: 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. It is demonstrated 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.


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[1] Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Croz, J. D.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D., LAPACK users’ guide, (1999), Society for Industrial and Applied Mathematics Philadelphia, PA · Zbl 0934.65030
[2] Basu, D., On statistics independent of a complete sufficient statistic, Sankhyā: The Indian Journal of Statistics (1933-1960), 15, 377-380, (1955) · Zbl 0068.13401
[3] Bos, C. S., Relating stochastic volatility estimation methods, (Handbook of Volatility Models and their Applications, (2012), John Wiley & Sons, Inc.), 147-174
[4] Carter, C. K.; Kohn, R., On Gibbs sampling for state space models, Biometrika, 81, 541-553, (1994) · Zbl 0809.62087
[5] 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
[6] Delatola, E.-I.; Griffin, J. E., Bayesian nonparametric modelling of the return distribution with stochastic volatility, Bayesian Analysis, 6, 901-926, (2011) · Zbl 1330.62116
[7] Durbin, J.; Koopman, S. J., A simple and efficient simulation smoother for state space time series analysis, Biometrika, 89, 603-615, (2002) · Zbl 1036.62071
[8] Eddelbuettel, D.; François, R., Rcpp: seamless R and C ++ integration, Journal of Statistical Software, 40, 1-18, (2011)
[9] Frühwirth-Schnatter, S., Data augmentation and dynamic linear models, Journal of Time Series Analysis, 15, 183-202, (1994) · Zbl 0815.62065
[10] Frühwirth-Schnatter, S., Efficient Bayesian parameter estimation, (Harvey, A.; Koopman, S. J.; Shephard, N., State Space and Unobserved Component Models: Theory and Applications, (2004), Cambridge University Press Cambridge), 123-151 · Zbl 05280144
[11] Frühwirth-Schnatter, S.; Sögner, L., Bayesian estimation of the Heston stochastic volatility model, Communications in Dependability and Quality Management, 11, 5-25, (2008)
[12] Frühwirth-Schnatter, S.; Wagner, H., Stochastic model specification search for gaussian and partially non-Gaussian state space models, Journal of Econometrics, 154, 85-100, (2010) · Zbl 1431.62373
[13] Gabriel, E., Fagg, G.E., Bosilca, G., Angskun, T., Dongarra, J.J., Squyres, J.M., Sahay, V., Kambadur, P., Barrett, B., Lumsdaine, A., Castain, R.H., Daniel, D.J., Graham, R.L., Woodall, T.S., 2004. Open MPI: goals, concept, and design of a next generation MPI implementation. In: Proceedings, 11th European PVM/MPI Users’ Group Meeting. Budapest, Hungary, pp. 97-104.
[14] Gelfand, A.; Sahu, S.; Carlin, B., Efficient parametrisations for normal linear mixed models, Biometrika, 82, 479-488, (1995) · Zbl 0832.62064
[15] Hull, J.; White, A., The pricing of options on assets with stochastic volatilities, The Journal of Finance, 42, 281-300, (1987)
[16] Ishihara, T.; Omori, Y., Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors, Computational Statistics and Data Analysis, 56, 3674-3689, (2012) · Zbl 1255.62066
[17] Jacquier, E.; Polson, N. G.; Rossi, P. E., Bayesian analysis of stochastic volatility models, Journal of Business & Economic Statistics, 12, 371-417, (1994)
[18] Kastner, G., 2013. stochvol: Efficient Bayesian inference for stochastic volatility (SV) models. R Package Version 0.5-0.
[19] 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
[20] L’Ecuyer, P.; Simard, R.; Chen, E. J.; Kelton, W. D., An object-oriented random-number package with many long streams and substreams, Operations Research, 50, 1073-1075, (2002)
[21] Liesenfeld, R.; Jung, R. C., Stochastic volatility models: conditional normality versus heavy-tailed distributions, Journal of Applied Econometrics, 15, 137-160, (2000)
[22] Liesenfeld, R.; Richard, J.-F., Classical and Bayesian analysis of univariate and multivariate stochastic volatility models, Econometric Reviews, 25, 335-360, (2006) · Zbl 1113.62130
[23] McCausland, W. J.; Miller, S.; Pelletier, D., Simulation smoothing for state space models: a computational efficiency analysis, Computational Statistics and Data Analysis, 55, 199-212, (2011) · Zbl 1247.62238
[24] Nakajima, J.; Omori, Y., Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew student’s-distribution, Computational Statistics and Data Analysis, 56, 3690-3704, (2012) · Zbl 1255.62319
[25] Omori, Y.; Chib, S.; Shephard, N.; Nakajima, J., Stochastic volatility with leverage: fast and efficient likelihood inference, Journal of Econometrics, 140, 425-449, (2007) · Zbl 1247.91207
[26] Pitt, M. K.; Shephard, N., Analytic convergence rates and parameterization issues for the Gibbs sampler applied to state space models, Journal of Time Series Analysis, 20, 63-85, (1999)
[27] Plummer, M.; Best, N.; Cowles, K.; Vines, K., CODA: convergence diagnosis and output analysis for MCMC, R News, 6, 7-11, (2006)
[28] R Development Core Team, R: A language and environment for statistical computing, (2012), R Foundation for Statistical Computing Vienna, Austria
[29] Roberts, G. O.; Papaspiliopoulos, O.; Dellaportas, P., Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes, Journal of the Royal Statistical Society: Series B, 66, 369-393, (2004) · Zbl 1062.62049
[30] Rue, H., Fast sampling of Gaussian Markov random fields, Journal of the Royal Statistical Society: Series B, 63, 325-338, (2001) · Zbl 0979.62075
[31] Shephard, N., Partial non-Gaussian state space, Biometrika, 81, 115-131, (1994) · Zbl 0796.62079
[32] Shephard, N.; Kim, S., [bayesian analysis of stochastic volatility models]: comment, Journal of Business & Economic Statistics, 12, 406-410, (1994)
[33] Shephard, N.; Pitt, M. K., Likelihood analysis of non-Gaussian measurement time series, Biometrika, 84, 653-667, (1997) · Zbl 0888.62095
[34] Strickland, C. M.; Martin, G. M.; Forbes, C. S., Parameterisation and efficient MCMC estimation of non-Gaussian state space models, Computational Statistics and Data Analysis, 52, 2911-2930, (2008) · Zbl 1452.62680
[35] Taylor, S. J., Financial returns modelled by the product of two stochastic processes—a study of daily sugar prices 1691-1679, (Anderson, O. D., Time Series Analysis: Theory and Practice 1, (1982), North-Holland), 203-226
[36] Tierney, L., Rossini, A.J., Li, N., Sevcikova, H., 2011. snow: Simple network of workstations. R Package Version 0.3-8.
[37] Tsiotas, G., On generalised asymmetric stochastic volatility models, Computational Statistics and Data Analysis, 56, 151-172, (2012) · Zbl 1241.91146
[38] Wang, J. J.; Chan, J. S.; Choy, S. B., Stochastic volatility models with leverage and heavy-tailed distributions: a Bayesian approach using scale mixtures, Computational Statistics and Data Analysis, 55, 852-862, (2011) · Zbl 1247.91152
[39] Yu, J., On leverage in a stochastic volatility model, Journal of Econometrics, 127, 165-178, (2005) · Zbl 1335.91116
[40] Yu, Y.; Meng, X.-L., To center or not to center: that is not the question—an ancillarity-suffiency interweaving strategy (ASIS) for boosting MCMC efficiency, Journal of Computational and Graphical Statistics, 20, 531-570, (2011)
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