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Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance

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2014-03
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Modelling covariance structures is known to suffer from the curse of dimensionality. In order to avoid this problem for forecasting, the authors propose a new factor multivariate stochastic volatility (fMSV) model for realized covariance measures that accommodates asymmetry and long memory. Using the basic structure of the fMSV model, the authors extend the dynamic correlation MSV model, the onditional/stochastic Wishart autoregressive models, the matrix-exponential MSV model, and the Cholesky MSV model. Empirical results for 7 financial asset returns for US stock returns indicate that the new fMSV models outperform existing dynamic conditional correlation models for forecasting future covariances. Among the new fMSV models, the Cholesky MSV model with long memory and asymmetry shows stable and better forecasting performance for one-day, five-day and ten-day horizons in the periods before, during and after the global financial crisis.
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JEL classifications: C32, C53, C58, G17 The authors are most grateful to Yoshi Baba for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, and Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science. Address for correspondence: Faculty of Economics, Soka University, 1-236 Tangi-cho, Hachioji, Tokyo 192-8577, Japan.
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Andersen, T.G., T. Bollerslev and N. Meddahi (2011), “Realized Volatility Forecasting and Market Microstructure Noise”, Journal of Econometrics, 160, 220–234. Asai, M. (2013), “Heterogeneous Asymmetric Dynamic Conditional Correlation Model with Stock Return and Range”, Journal of Forecasting, 32, 469–480. Asai, M. and M. McAleer (2006), “Asymmetric Multivariate Stochastic Volatility”, Econometric Reviews, 25, 453–473. Asai, M. and M. McAleer (2009a), “The Structure of Dynamic Correlations in Multivariate Stochastic Volatility Models”, Journal of Econometrics, 150, 182–192. Asai, M. and M. McAleer (2009b), “Multivariate Stochastic Volatility, Leverage and News Impact Surfaces”, Econometrics Journal, 12, 292–309. Asai, M., M. McAleer, and J. Yu (2006), “Multivariate Stochastic Volatility: A Review”, Econometric Reviews, 25, 145–175. Asai, M. and M.K.P. So (2013), “Stochastic Covariance Models”, Journal of Japan Statistical Society, 43, 127–162. Asai, M. and M.K.P. So (2014), “Long Memory and Asymmetry for Matrix-Exponential Dynamic Correlation Processes”, Working Paper, Faculty of Economics, Soka University. Baillie R.T., T. Bollerslev and H.O. Mikkelsen (1996), “Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 74, 3–30. Barndorff-Nielsen, O.E., P.R. Hansen, A. Lunde, and N. Shephard (2008), “Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise”, Econometrica, 76, 1481–1536. Barndorff-Nielsen, O.E., P.R. Hansen, A. Lunde, and N. Shephard (2011), “Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of The Covariation of Equity Prices with Noise and Non-Synchronous Trading”, Journal of Econometrics, 162, 149–169. Barndorff-Nielsen, O.E. and N. Shephard (2002), “Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models”, Journal of the Royal Statistical Society, Series B, 64, 253–280. Bauer, G.H. and K. Vorkink (2011), “Forecasting Multivariate Realized Stock Market Volatility”, Journal of Econometrics, 160, 93–101. Bauwens, L., S. Laurent, and J.V.K. Rombouts (2006), “Multivariate GARCH Models: A Survey”, Journal of Applied Econometrics, 21, 79–109. Bickel, P. J., and E. Levina (2008a), “Regularized Estimation of Large Covariance Matrices”, Annals of Statistics, 36, 199–277. Bickel, P. J., and E. Levina (2008b), “Covariance Regularization by Thresholding”, Annals of Statistics, 36, 2577–2604. Bollerslev, T. and H.O. Mikkelsen (1996), “Modeling and Pricing Long-Memory in Stock Market Volatility”, Journal of Econometrics, 73, 151–184. Bollerslev, T., N. Sizova, and G. Tauchen (2011), “Volatility in Equilibrium: Asymmetries and Dynamic Dependencies”, Review of Finance, 16, 31–80. Bollerslev, T. and V. Todorov (2011), “Tails, Fears, and Risk Premia”, Journal of Finance, 66, 2165–2211. Bollerslev, T., and H. Zhou (2002), “Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility”, Journal of Econometrics, 109, 33–65. Breidt, F.J., N. Crato and P. de Lima (1998), “The Detection and Estimation of Long Memory”, Journal of Econometrics, 83, 325–348. Caporin, M., and M. McAleer (2011), “Threshold, News Impact Surfaces and Dynamic Asymmetric Multivariate GARCH”, Statistica Neerlandica, 65, 125–163. Cappiello, L., R.F. Engle and K. Sheppard (2006), “Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns”, Journal of Financial Econometrics, 4, 537–572. Chen, X. and E. Ghysels (2010), “News - Good or Bad - and Its Impact on Volatility Predictions over Multiple Horizons”, Review of Financial Studies, 24, 46–81. Chiriac, R., and V. Voev (2011), “Modelling and Forecasting Multivariate Realized Volatility”, Journal of Applied Econometrics, 26, 922–947. Chib, S., F. Nardari, and N. Shephard (2006), “Analysis of High Dimensional Multivariate Stochastic Volatility Models”, Journal of Econometrics, 134, 341–371. Chib, S., Y. Omori, and M. Asai (2009), “Multivariate Stochastic Volatility”, In T. G. Andersen, R.A. Davis, J.P. Kreiss, and T. Mikosch (Eds.), Handbook of Financial Time Series, pp.365–400, New York: Springer-Verlag. Chiu, T.Y.M., T. Leonard and K.W. Tsui (1996), “The Matrix-Logarithmic Covariance Model”, Journal of the American Statistical Association, 91, 198–210. Christensen, K., S. Kinnebrock and M. Podolskij (2010), “Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data”, Journal of Econometrics, 159, 116–133. Corsi, F. (2009), “A Simple Approximate Long-Memory Model of Realized Volatility, Journal of Financial Econometrics, 7, 174–196. Corsi, F., and R. Ren`o (2010), “HAR Volatility Modelling with Heterogeneous Leverage and Jumps”, Unpublished Paper, Universit`a di Siena. Diebold, F.X., and M. Nerlove (1989), “The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model”, Journal of Applied Econometrics, 4, 1–21. Ding, Z. and Engle, R. F. (2001), “Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing”, Academia Economic Papers, 29, 157–184. Durbin, J. and S.J. Koopman (1997), “Monte Carlo Maximum Likelihood Estimation for Non-Gaussian State Space Models”, Biometrika, 84, 669-684. Engle, R.F. (2002), “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models”, Journal of Business & Economic Statistics, 20, 339–350. Engle, R.F. and K.F. Kroner (1995), “Multivariate Simultaneous Generalized ARCH”, Econometric Theory, 11, 122–150. Engle, R.F., and V. Ng (1993), “Measuring and Testing the Impact of News on Volatility”, Journal of Finance, 48, 1749–1778. Gallant, A.R., and G. Tauchen (1996), “Which Moments to Match?”, Econometric Theory, 12, 657–681. Glosten, L., R. Jagannathan, and D. Runkle (1992), “On the Relation between the Expected Value and Volatility of Nominal Excess Returns on Stocks”, Journal of Finance, 46, 1779–1801. Golosnoy, V., B. Gribisch, and R. Liesenfeld (2012), “The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility”, Journal of Econometrics, 167, 211–223. Gourieroux, C., J. Jasiak, and R. Sufana (2009), “The Wishart Autoregressive Process of Multivariate Stochastic Volatility”, Journal of Econometrics, 150, 167–181. Griffin, J.E., and R.C.A. Oomen (2011), “Covariance Measurement in the Presence of Non-Synchronous Trading and Market Microstructure Noise”, Journal of Econometrics, 160, 58–68. Hautsch, N., R.M. Kyj and R.C.A. Oomen (2012), “A Blocking and Regularization Approach to High Dimensional Realized Covariance Estimation”, Journal of Applied Econometrics, 27, 625–645. Hansen, P.R., Z. Huang, and H.H. Shek (2012), “Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility”, Journal of Applied Econometrics, 27, 877–906. Harvey, A. (1998), “Long Memory in Stochastic Volatility”, In: Knight, J. and S. Satchell (eds.), Forecasting Volatility in Financial Markets, Oxford: Butterworth-Haineman, 307–320. Harvey, A.C., E. Ruiz, and N. Shephard (1994), “Multivariate Stochastic Variance Models”, Review of Economic Studies, 61, 247–264. Ishihara, T., Y. Omori and M. Asai (2012), “Matrix Exponential Stochastic Volatility with Cross Leverage”, Working paper, Faculty of Economics, University of Tokyo. Jacquier, E., N.G. Polson, and P.E. Rossi (1994), “Bayesian Analysis of Stochastic Volatility Models” (with discussion), Journal of Business & Economic Statistics, 12, 371–389. Johnstone, I.M., and A.Y. Lu (2009), “On Consistency and Sparsity for Principal Component Analysis in High Dimensions” (with discussions), Journal of the American Statistical Association, 104, 682–703. Kawakatsu, H. (2006), “Matrix Exponential GARCH”, Journal of Econometrics, 134, 95–128. Kroner, K. and V. Ng (1998), “Modeling Asymmetric Comovements of Asset Returns”, Review Financial Studies, 11, 817–844. Lanne, M., and P. Saikkonen (2007), “A Multivariate Generalized Orthogonal Factor GARCH Model”, Journal of Business & Economic Statistics, 25, 61–75. Laurent, S., J.V.K. Rombouts and F. Violante (2012), “On the Forecasting Accuracy of Multivariate GARCH Models”, Journal of Applied Econometrics, 27, 934–955. Liesenfeld, R., and J.-F. Richard (2003), “Univariate and Multivariate Stochastic Volatility Models: Estimation and Diagnostics”, Journal of Empirical Finance, 10, 505–531. Martens, M., D. van Dijk, and M. de Pooter (2009), “Forecasting S&P 500 Volatility: Long Memory, Level Shifts, Leverage Effects, Day-of-the-Week Seasonality, and Macroeconomic Announcements”, International Journal of Forecasting, 25, 282–303. Nelson, D.B. (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, 59, 347–370. Pérez, A. and E. Ruiz (2001), “Finite Sample Properties of a QML Estimator of Stochastic Volatility Models with Long Memory”, Economics Letters, 70, 157–164. Philipov, A. and M.E. Glickman (2006a), “Factor Multivariate Stochastic Volatility via Wishart Processes”, Econometric Reviews, 25, 311–334. Philipov, A. and M.E. Glickman (2006b), “Multivariate Stochastic Volatility via Wishart Processes”, Journal of Business & Economic Statistics, 24, 313–328. Pitt, M.K. and N. Shephard (1999), “Time Varying Covariances: A Factor Stochastic Volatility Approach”, In J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith (Eds.), Bayesian Statistics, Volume 6, pp.547–570, Oxford: Oxford University Press. Ray, B.K., and R.S. Tsay (2000), “Long-Range Dependence in Daily Stock Volatilities”, Journal of Business & Economic Statistics, 18, 254–262. Sandmann, G. and S.J. Koopman (1998), “Estimation of Stochastic Volatility Models via Monte Carlo Maximum Likelihood”, Journal of Econometrics, 87, 271–301. Sheena (2013), “Modified Estimators of the Contribution Rates of Population Eigenvalues”, Journal of Multivariate Analysis, 115, 301–316. Shimotsu, K. (2007), “Gaussian Semiparametric Estimation of Multivariate Fractionally Integrated Processes”, Journal of Econometrics, 137, 277–310. Shimotsu, K. and P.C.B Phillips (2006), “Local Whittle Estimation of Fractional Integration and Some of Its Variants”, Journal of Econometrics, 130, 209–233. Silvennoinen, A., and T. Ter¨asvirta (2009), “Multivariate GARCH Models”, In T. G. Andersen, R.A. Davis, J.-P. Kreiss, and T. Mikosch (eds.), slHandbook of Financial Time Series, 201–229, New York: Springer. So, M.K.P. (2002), “Bayesian Analysis of Long Memory Stochastic Volatility Models”, Sankhy¯a, 24, 1–10. So, M.K.P. and S.W.Y. Kwok (2006), “A Multivariate Long Memory Stochastic Volatility Model”, Physica A, 362, 450–464. Sugiyama, T and H. Tong (1976), “On A Statistic Useful for Dimensionality Reduction of Linear Stochastic Systems”, Communications in Statistics: Theory and Methods, 5, 711–721. Tao, M., Y. Wang, Q. Yao and J. Zou (2011), “Large Volatility Matrix Inference via Combining Low-Frequency and High-Frequency Approaches”, Journal of the American Statistical Association, 106, 1025–1040. Vrontos, I.D., P. Dellaportas, and D.N. Politis (2003), “A Full-Factor Multivariate GARCH Model”, 6, 311–333. Wang, Y., J. and Zou (2010), “Vast Volatility Matrix Estimation for High-Frequency Financial Data”, Annals of Statistics, 38, 943–978. Yu, J. (2005), “On Leverage in a Stochastic Volatility Model”, Journal of Econometrics, 127, 165–178. Zhang, L. (2011), “Estimating Covariation: Epps Effect, Microstructure Noise”, Journal of Econometrics, 160, 33–47.