A partial correlation vine based approach for modeling and forecasting multivariate volatility time-series

A novel approach for dynamic modeling and forecasting of realized covariance matrices is proposed. Realized variances and realized correlation matrices are jointly estimated. The one-to-one relationship between a positive definite correlation matrix and its associated set of partial correlations corresponding to any vine specification is used. A method to select a vine structure, which allows for parsimonious time-series modeling, is introduced. The predicted partial correlations have a clear practical interpretation. Being algebraically independent they do not underlie any algebraic constraint. The forecasting performance is evaluated through investigation of six-dimensional real data and is compared to Cholesky decomposition based benchmark models.

[1]  R. Engle.  Dynamic Conditional Correlation , 2002 .

[2]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[3]  Valeri Voev.  Dynamic Modelling of Large Dimensional Covariance Matrices , 2007 .

[4]  Andrew J. Patton.  Volatility Forecast Comparison Using Imperfect Volatility Proxies , 2006 .

[5]  Claudia Czado,et al.  Pair-Copula Constructions of Multivariate Copulas , 2010 .

[6]  Harry Joe,et al.  Truncation of vine copulas using fit indices , 2015, J. Multivar. Anal..

[7]  Peter Reinhard Hansen,et al.  The Model Confidence Set , 2010 .

[8]  Regular vines : generation algorithm and number of equivalence classes , 2011 .

[9]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[10]  U. Cherubini,et al.  RiskMetrics Technical Document , 2015 .

[11]  Mark Podolskij,et al.  Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data , 2010 .

[12]  Dorota Kurowicka,et al.  Generating random correlation matrices based on vines and extended onion method , 2009, J. Multivar. Anal..

[13]  N. Yoshida,et al.  On covariance estimation of non-synchronously observed diffusion processes , 2005 .

[14]  Vasyl Golosnoy,et al.  The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility , 2010 .

[15]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[16]  M. Steel,et al.  On Bayesian Modelling of Fat Tails and Skewness , 1998 .

[17]  H. Joe.  Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .

[18]  T. W. Anderson,et al.  An Introduction to Multivariate Statistical Analysis , 1959 .

[19]  R. Cooke,et al.  About the number of vines and regular vines on n nodes , 2010 .

[20]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[21]  Gregory H. Bauer,et al.  Forecasting multivariate realized stock market volatility , 2011 .

[22]  F. Diebold,et al.  VOLATILITY AND CORRELATION FORECASTING , 2006 .

[23]  J. Jacod.  Limit of Random Measures Associated with the Increments of a Brownian Semimartingale , 2018 .

[24]  S. Mittnik,et al.  The Volatility of Realized Volatility , 2005 .

[25]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[26]  E. Brechmann,et al.  A multivariate volatility vine copula model , 2015 .

[27]  R. Cooke,et al.  Completion problem with partial correlation vines , 2006 .

[28]  Jeroen V.K. Rombouts,et al.  Série Scientifique Scientific Series on Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models on Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models , 2022 .

[29]  Toshihide Ibaraki,et al.  An Algorithm for Finding K Minimum Spanning Trees , 1981, SIAM J. Comput..

[30]  T. Bedford,et al.  Vines: A new graphical model for dependent random variables , 2002 .

[31]  George C. Tiao,et al.  Kurtosis of GARCH and stochastic volatility models with non-normal innovations , 2003 .

[32]  Claudia Czado,et al.  Simplified pair copula constructions - Limitations and extensions , 2013, J. Multivar. Anal..

[33]  H. Joe.  Generating random correlation matrices based on partial correlations , 2006 .

[34]  C. Doléans-Dade,et al.  Intégrales stochastiques par rapport aux martingales locales , 1970 .

[35]  Valeri Voev,et al.  Forecasting Covariance Matrices : A Mixed Approach , 2016 .

[36]  H. Joe.  Asymptotic efficiency of the two-stage estimation method for copula-based models , 2005 .

[37]  H. Joe,et al.  The Estimation Method of Inference Functions for Margins for Multivariate Models , 1996 .

[38]  Fulvio Corsi,et al.  A Simple Approximate Long-Memory Model of Realized Volatility , 2008 .

[39]  Dorota Kurowicka,et al.  Dependence Modeling: Vine Copula Handbook , 2010 .

[40]  C. Gouriéroux,et al.  The Wishart Autoregressive Process of Multivariate Stochastic Volatility , 2009 .

[41]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[42]  Kjersti Aas,et al.  On the simplified pair-copula construction - Simply useful or too simplistic? , 2010, J. Multivar. Anal..

[43]  N. Shephard,et al.  Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics , 2004 .

[44]  Lan Zhang.  Estimating Covariation: Epps Effect, Microstructure Noise , 2006 .

[45]  Harry Joe,et al.  Parsimonious parameterization of correlation matrices using truncated vines and factor analysis , 2014, Comput. Stat. Data Anal..

[46]  R. Engle,et al.  Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns , 2003, SSRN Electronic Journal.

[47]  P. Hansen,et al.  Realized GARCH: A Joint Model of Returns and Realized Measures of Volatility , 2010 .

[48]  R. Cooke,et al.  A parameterization of positive definite matrices in terms of partial correlation vines , 2003 .

[49]  Jessika Weiss,et al.  Graphical Models In Applied Multivariate Statistics , 2016 .

[50]  R. Gencay,et al.  An Introduc-tion to High-Frequency Finance , 2001 .

[51]  B. Poignard.  New approaches for high-dimensional multivariate GARCH models , 2017 .

[52]  Roxana Halbleib,et al.  Modelling and Forecasting Multivariate Realized Volatility , 2008 .

[53]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

[54]  H. Joe.  Dependence Modeling with Copulas , 2014 .