Analysis of high dimensional multivariate stochastic volatility models
This paper is concerned with the fitting and comparison of high dimensional multivariate time series models with time varying correlations. The models considered here combine features of the classical factor model with those of the univariate stochastic volatility model. Specifically, a set of unobserved time-dependent factors, along with an associated loading matrix, are used to model the contemporaneous correlation while, conditioned on the factors, the noise in each factor and each series is assumed to follow independent three-parameter univariate stochastic volatility processes. A complete analysis of these models, and its special cases, is developed that encompasses estimation, filtering and model choice. The centerpieces of our estimation algorithm (which relies on MCMC methods) is (1) a reduced blocking scheme for sampling the free elements of the loading matrix and the factors and (2) a special method for sampling the parameters of the univariate SV process. The sampling of the loading matrix (containing typically many hundreds of parameters) is done via a highly tuned Metropolis-Hastings step. The resulting algorithm is completely scalable in terms of series and factors and very simulation-efficient. We also provide methods for estimating the log-likelihood function and the filtered values of the time-varying volatilities and correlations. We pay special attention to the problem of comparing one version of the model with another and for determining the number of factors. For this purpose we use MCMC methods to find the marginal likelihood and associated Bayes factors of each fitted model. In sum, these procedures lead to the first unified and practical likelihood based analysis of truly high dimensional models of stochastic volatility. We apply our methods in detail to two datasets. The first is the return vector on 20 exchange rates against the US Dollar. The second is the return vector on 40 common stocks quoted on the New York Stock Exchange.
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- Eric Ghysels & Andrew Harvey & Éric Renault, 1995.
CIRANO Working Papers
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- Robert F. Engle & Kevin Sheppard, 2001.
"Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH,"
NBER Working Papers
8554, National Bureau of Economic Research, Inc.
- Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
- Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003.
"Flexible Multivariate GARCH Modeling with an Application to International Stock Markets,"
The Review of Economics and Statistics,
MIT Press, vol. 85(3), pages 735-747, August.
- Ledoit, Olivier & Santa-Clara, Pedro & Wolf, Michael, 1999. "Flexible Multivariate GARCH Modeling With an Application to International Stock Markets," University of California at Los Angeles, Anderson Graduate School of Management qt93s6p8gb, Anderson Graduate School of Management, UCLA.
- Olivier Ledoit & Pedro Santa Clara & Michael Wolf, 2001. "Flexible multivariate GARCH modeling with an application to international stock markets," Economics Working Papers 578, Department of Economics and Business, Universitat Pompeu Fabra.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
- John Geweke & Guofu Zhou, 1996.
"Measuring the Pricing Error of the Arbitrage Pricing Theory,"
CEMA Working Papers
276, China Economics and Management Academy, Central University of Finance and Economics.
- Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-87.
- John F. Geweke & Guofu Zhou, 1995. "Measuring the pricing error of the arbitrage pricing theory," Staff Report 189, Federal Reserve Bank of Minneapolis.
- Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
- Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
- Chib, Siddhartha & Greenberg, Edward, 1996.
"Markov Chain Monte Carlo Simulation Methods in Econometrics,"
Cambridge University Press, vol. 12(03), pages 409-431, August.
- Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003.
"Modeling and Forecasting Realized Volatility,"
Econometric Society, vol. 71(2), pages 579-625, March.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
- Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990.
"Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills,"
Journal of Econometrics,
Elsevier, vol. 45(1-2), pages 213-237.
- Robert F. Engle & Victor Ng & Michael Rothschild, 1988. "Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills," NBER Technical Working Papers 0065, National Bureau of Economic Research, Inc.
- King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994.
"Volatility and Links between National Stock Markets,"
Econometric Society, vol. 62(4), pages 901-33, July.
- Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
- Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
- Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
- Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
- Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
- Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
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