Singular Conditional Autoregressive Wishart Model for Realized Covariance Matrices

References

• Alfelt, G., Bodnar, T., and Tyrcha, J. (2020), “Goodness-of-Fit Tests for Centralized Wishart Processes,” Communications in Statistics – Theory and Methods, 49, 5060–5090.
   Web of Science ®Google Scholar
• Anatolyev, S., and Kobotaev, N. (2018), “Modeling and Forecasting Realized Covariance Matrices with Accounting for Leverage,” Econometric Reviews, 37, 114–139.
   Web of Science ®Google Scholar
• Andersen, T. G., Bollerslev, T., Diebold, F. X., and Labys, P. (2003), “Modeling and Forecasting Realized Volatility,” Econometrica, 71, 579–625. DOI: 10.1111/1468-0262.00418.
   Web of Science ®Google Scholar
• Ao, M., Yingying, L., and Zheng, X. (2019), “Approaching Mean-Variance Efficiency for Large Portfolios,” The Review of Financial Studies, 32, 2890–2919. DOI: 10.1093/rfs/hhy105.
   Web of Science ®Google Scholar
• Archakov, I., Hansen, P. R., and Lunde, A. (2020), “A Multivariate Realized GARCH Model,” available at https://sites.google.com/site/peterreinhardhansen/research-papers/amultivariaterealizedgarchmodel
   Google Scholar
• Asai, M., McAleer, M., and Yu, J. (2006), “Multivariate Stochastic Volatility: A Review,” Econometric Reviews, 25, 145–175. DOI: 10.1080/07474930600713564.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., Mykland, P. A., and Zhang, L. (2011), “Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise,” Journal of Econometrics, 160, 160–175. DOI: 10.1016/j.jeconom.2010.03.028.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Yu, J. (2009), “High Frequency Market Microstructure Noise Estimates and Liquidity Measures,” Annals of Applied Statistics, 3, 422–457.
   Web of Science ®Google Scholar
• Bandi, F. M., Kolokolov, A., Pirino, D., and Renò, R. (2020a), “Realized Moments: Identification and Pricing,” working paper.
   Google Scholar
• Bandi, F. M., Kolokolov, A., Pirino, D., and Renò, R. (2020b), “Zeros,” Management Science, 66, 3466–3479.
   Web of Science ®Google Scholar
• Bandi, F. M., Pirino, D., and Renò, R. (2017), “Excess Idle Time,” Econometrica, 85, 1793–1846. DOI: 10.3982/ECTA13595.
   Web of Science ®Google Scholar
• Bandi, F. M., and Russell, J. R. (2006), “Separating Microstructure Noise from Volatility,” Journal of Financial Economics, 79, 655–692. DOI: 10.1016/j.jfineco.2005.01.005.
   Web of Science ®Google Scholar
• Bandi, F. M., and Russell, J. R. (2008), “Microstructure Noise, Realized Variance, and Optimal Sampling,” The Review of Economic Studies, 75, 339–369.
   Web of Science ®Google Scholar
• Barndorff-Nielsen, O. E., and Shephard, N. (2004), “Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics,” Econometrica, 72, 885–925.
   Web of Science ®Google Scholar
• Bauwens, L., Laurent, S., and Rombouts, J. V. (2006), “Multivariate GARCH Models: A Survey,” Journal of Applied Econometrics, 21, 79–109. DOI: 10.1002/jae.842.
   Web of Science ®Google Scholar
• BenSaïda, A. (2017), “Herding Effect on Idiosyncratic Volatility in U.S. Industries,” Finance Research Letters, 23, 121–132.
   Web of Science ®Google Scholar
• Bibinger, M., Hautsch, N., Malec, P., and Reiß, M. (2014), “Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency,” The Annals of Statistics, 42, 1312–1346.
   Web of Science ®Google Scholar
• Bibinger, M., Hautsch, N., Malec, P., and Reiss, M. (2019), “Estimating the Spot Covariation of Asset Prices-Statistical Theory and Empirical Evidence,” Journal of Business & Economic Statistics, 37, 419–435.
   Web of Science ®Google Scholar
• Bodnar, O., Bodnar, T., and Parolya, N. (2022), “Recent Advances in Shrinkage-Based High-dimensional Inference,” Journal of Multivariate Analysis, 188, 104826. DOI: 10.1016/j.jmva.2021.104826.
   Web of Science ®Google Scholar
• Bodnar, T., Dmytriv, S., Okhrin, Y., Parolya, N., and Schmid, W. (2021), “Statistical Inference for the Expected Utility Portfolio in High Dimensions,” IEEE Transactions on Signal Processing, 69, 1–14. DOI: 10.1109/TSP.2020.3037369.
   Web of Science ®Google Scholar
• Bodnar, T., Dmytriv, S., Parolya, N., and Schmid, W. (2019), “Tests for the Weights of the Global Minimum Variance Portfolio in a High-dimensional Setting,” IEEE Transactions on Signal Processing, 67, 4479–4493.
   Web of Science ®Google Scholar
• Bodnar, T., Mazur, S., and Okhrin, Y. (2014), “Distribution of the Product of Singular Wishart Matrix and Normal Vector,” Theory of Probability and Mathematical Statistics, 91, 1–15.
   Google Scholar
• Bodnar, T., and Okhrin, Y. (2008), “Properties of the Singular, Inverse and Generalized Inverse Partitioned Wishart Distributions,” Journal of Multivariate Analysis, 99, 2389–2405.
   Web of Science ®Google Scholar
• Bodnar, T., Okhrin, Y., and Parolya, N. (2022), “Optimal Shrinkage-based Portfolio Selection in High Dimensions,” Journal of Business & Economic Statistics, to appear, DOI: 10.1080/07350015.2021.2004897.
   Google Scholar
• Bodnar, T., Parolya, N., and Schmid, W. (2018), “Estimation of the Global Minimum Variance Portfolio in High Dimensions,” European Journal of Operational Research, 266, 371–390. DOI: 10.1016/j.ejor.2017.09.028.
   Web of Science ®Google Scholar
• Buccheri, G., Bormetti, G., Corsi, F., and Lillo, F. (2021), “A Score-driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics,” Journal of Business & Economic Statistics, 39, 920–936.
   Web of Science ®Google Scholar
• Cai, T. T., Hu, J., Li, Y., and Zheng, X. (2020), “High-dimensional Minimum Variance Portfolio Estimation based on High-frequency Data,” Journal of Econometrics, 214, 482–494.
   Web of Science ®Google Scholar
• Catania, L., Mari, R. D., and de Magistris, P. S. (2020), “Dynamic Discrete Mixtures for High-Frequency Prices,” Journal of Business & Economic Statistics, 40, 559–577.
   Web of Science ®Google Scholar
• Chan, L. K., Lakonishok, J., and Swaminathan, B. (2007), “Industry Classifications and Return Comovement,” Financial Analysts Journal, 63, 56–70. DOI: 10.2469/faj.v63.n6.4927.
   Web of Science ®Google Scholar
• Christensen, K., Oomen, R. C., and Podolskij, M. (2014), “Fact or Friction: Jumps at Ultra High Frequency,” Journal of Financial Economics, 114, 576–599. DOI: 10.1016/j.jfineco.2014.07.007.
   Web of Science ®Google Scholar
• Corsi, F. (2009), “A Simple Approximate Long-Memory Model of Realized Volatility,” Journal of Financial Econometrics, 7, 174–196.
   Web of Science ®Google Scholar
• Corsi, F., Peluso, S., and Audrino, F. (2015), “Missing in Asynchronicity: A Kalman-em Approach for Multivariate Realized Covariance Estimation,” Journal of Applied Econometrics, 30, 377–397.
   Web of Science ®Google Scholar
• de Brito, D., Medeiros, M., and Ribeiro, R. (2018), “Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage,” working paper.
   Google Scholar
• De Nard, G., Engle, R., Ledoit, O., and Wolf, M. (2020), “Large Dynamic Covariance Matrices: Enhancements based on Intraday Data,” working paper.
   Google Scholar
• DeMiguel, V., Garlappi, L., and Uppal, R. (2009), “Optimal Versus Naive Diversification: How Inefficient is the 1/n Portfolio Strategy?” The Review of Financial Studies, 22, 1915–1953.
   Web of Science ®Google Scholar
• Ding, Y., Li, Y., and Zheng, X. (2021), “High Dimensional Minimum Variance Portfolio Estimation Under Statistical Factor Models,” Journal of Econometrics, 222, 502–515.
   Web of Science ®Google Scholar
• Engle, R. F. (2000), “The Econometrics of Ultra-High-Frequency Data,” Econometrica, 68, 1–22.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Engle, R., and Mezrich, J. (1996), “GARCH for Groups,” Risk, 9, 36–40.
   Google Scholar
• Engle, R. F., and Kroner, K. F. (1995), “Multivariate Simultaneous Generalized ARCH,” Econometric Theory, 11, 122–150. DOI: 10.1017/S0266466600009063.
   Web of Science ®Google Scholar
• Engle, R. F., Ledoit, O., and Wolf, M. (2019), “Large Dynamic Covariance Matrices,” Journal of Business & Economic Statistics, 37, 363–375.
   Web of Science ®Google Scholar
• Frahm, G., and Memmel, C. (2010), “Dominating Estimators for Minimum-Variance Portfolios,” Journal of Econometrics, 159, 289–302. DOI: 10.1016/j.jeconom.2010.07.007.
   Web of Science ®Google Scholar
• Glombeck, K. (2014), “Statistical Inference for High-dimensional Global Minimum Variance Portfolios,” Scandinavian Journal of Statistics, 41, 845–865.
   Web of Science ®Google Scholar
• Golosnoy, V., Gribisch, B., and Liesenfeld, R. (2012), “The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility,” Journal of Econometrics, 167, 211–223.
   Web of Science ®Google Scholar
• Gouriéroux, C., Jasiak, J., and Sufana, R. (2009), The Wishart Autoregressive Process of Multivariate Stochastic Volatility,” Journal of Econometrics, 150, 167–181.
   Web of Science ®Google Scholar
• Gupta, A. K., and Nagar, D. K. (2000), Matrix Variate Distributions, Boca Raton, FL: CRC Press.
   Google Scholar
• Hansen, P. R., Lunde, A., and Nason, J. M. (2011), “The Model Confidence Set,” Econometrica, 79, 453–497.
   Web of Science ®Google Scholar
• Harville, D. (1997), Matrix Algebra from Statistician’s Perspective, New York: Springer.
   Google Scholar
• Hautsch, N., Kyj, L. M., and Malec, P. (2015), “Do High-Frequency Data Improve High-Dimensional Portfolio Allocations?” Journal of Applied Econometrics, 30, 263–290. DOI: 10.1002/jae.2361.
   Web of Science ®Google Scholar
• Jacod, J., and Podolskij, M. (2013), “A Test for the Rank of the Volatility Process: The Random Perturbation Approach,” The Annals of Statistics, 41, 2391–2427.
   Web of Science ®Google Scholar
• Jin, X., and Maheu, J. M. (2012), “Modeling Realized Covariances and Returns,” Journal of Financial Econometrics, 11, 335–369. DOI: 10.1093/jjfinec/nbs022.
   Web of Science ®Google Scholar
• King, B. F. (1966), “Market and Industry Factors in Stock Price Behavior,” The Journal of Business, 39, 139–190. DOI: 10.1086/294847.
   Web of Science ®Google Scholar
• Ledoit, O., and Wolf, M. (2011), Robust Performances Hypothesis Testing With the Variance, Wilmott, 2011, 86–89.
   Google Scholar
• Ledoit, O., and Wolf, M. (2017), “Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks,” The Review of Financial Studies, 30, 4349–4388.
   Web of Science ®Google Scholar
• Ledoit, O., and Wolf, M. (2020), “The Power of (non-)linear Shrinking: A Review and Guide to Covariance Matrix Estimation,” working paper.
   Google Scholar
• Litimi, H., BenSaïda, A., and Bouraoui, O. (2016), Herding and Excessive Risk in the American Stock Market: A Sectoral Analysis,” Research in International Business and Finance, 38, 6–21. DOI: 10.1016/j.ribaf.2016.03.008.
   Web of Science ®Google Scholar
• Lütkepohl, H. (2005), The New Introduction to Multiple Time Series Analysis, Berlin: Springer.
   Google Scholar
• Noureldin, D., Shephard, N., and Sheppard, K. (2012), Multivariate High-Frequency-based Volatility (HEAVY) Models,” Journal of Applied Econometrics, 27, 907–933. DOI: 10.1002/jae.1260.
   Web of Science ®Google Scholar
• Noureldin, D., Sheppard, K., and Shephard, N. (2014), Multivariate Rotated ARCH Models,” Journal of Econometrics, 179, 16–30. DOI: 10.1016/j.jeconom.2013.10.003.
   Web of Science ®Google Scholar
• Pedersen, R. S., and Rahbek, A. (2014), “Multivariate Variance Targeting in the BEKK-GARCH Model,” The Econometrics Journal, 17, 24–55. DOI: 10.1111/ectj.12019.
   Web of Science ®Google Scholar
• Rubio, F., Mestre, X., and Palomar, D. P. (2012), “Performance Analysis and Optimal Selection of Large Minimum Variance Portfolios Under Estimation Risk,” IEEE Journal of Selected Topics in Signal Processing, 6, 337–350. DOI: 10.1109/JSTSP.2012.2202634.
   Web of Science ®Google Scholar
• Shephard, N., and Xiu, D. (2017), “Econometric Analysis of Multivariate Realised qml: Estimation of the Covariation of Equity Prices Under Asynchronous Trading,” Journal of Econometrics, 201, 19–42.
   Web of Science ®Google Scholar
• Srivastava, M. (2003), “Singular Wishart and Multivariate Beta Distributions,” The Annals of Statistics, 31, 1537–1560. DOI: 10.1214/aos/1065705118.
   Web of Science ®Google Scholar
• Sucarrat, G., and Grønneberg, S. (2020), “Risk Estimation with a Time-Varying Probability of Zero Returns,” Journal of Financial Econometrics, 20, 278–309.
   Web of Science ®Google Scholar
• Yu, P. L., Li, W., and Ng, F. (2017), “The Generalized Conditional Autoregressive Wishart Model for Multivariate Realized Volatility,” Journal of Business & Economic Statistics, 35, 513–527.
   Web of Science ®Google Scholar