High-Dimensional Copula-Based Distributions with Mixed Frequency Data

This paper proposes a new model for high-dimensional distributions of asset returns that utilizes mixed frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, enabling the use of high frequency data to accurately forecast linear dependence, and a new class of copulas designed to capture nonlinear dependence among the resulting uncorrelated, low frequency, residuals. Estimation of the new class of copulas is conducted using composite likelihood, facilitating applications involving hundreds of variables. In- and out-of-sample tests confirm the superiority of the proposed models applied to daily returns on constituents of the S&P 100 index.

[1]  N. Shephard,et al.  Realized Kernels in Practice: Trades and Quotes , 2009 .

[2]  Halbert White,et al.  Tests of Conditional Predictive Ability , 2003 .

[3]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[4]  N. Hautsch,et al.  Do High-Frequency Data Improve High-Dimensional Portfolio Allocations? , 2013 .

[5]  M. Rockinger,et al.  On the Importance of Time Variability in Higher Moments for Asset Allocation , 2010 .

[6]  Andrew J. Patton,et al.  Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads , 2013 .

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

[8]  C. Varin,et al.  A note on composite likelihood inference and model selection , 2005 .

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

[10]  N. Hautsch,et al.  Do High-Frequency Data Improve High-Dimensional Portfolio Allocations?: HF DATA AND HIGH-DIMENSIONAL PORTFOLIOS , 2015 .

[11]  Ruey S. Tsay,et al.  High Dimensional Dynamic Stochastic Copula Models , 2014 .

[12]  T. Bollerslev,et al.  Roughing up Beta: Continuous versus Discontinuous Betas and the Cross Section of Expected Stock Returns , 2016 .

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

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

[15]  N. Reid,et al.  AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS , 2011 .

[16]  S. Li.  Continuous Beta, Discontinuous Beta, and the Cross-Section of Expected Stock Returns∗ , 2012 .

[17]  Neil Shephard,et al.  Multivariate High-Frequency-Based Volatility (HEAVY) Models , 2012 .

[18]  N. Shephard,et al.  Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics , 2002 .

[19]  Q. Vuong.  Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses , 1989 .

[20]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[21]  Andrew J. Patton.  Copula Methods for Forecasting Multivariate Time Series , 2013 .

[22]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[23]  Tae-Hwy Lee,et al.  Copula-based multivariate GARCH model with uncorrelated dependent errors , 2009 .

[24]  Robert F. Engle,et al.  Fitting Vast Dimensional Time-Varying Covariance Models , 2017, Journal of Business & Economic Statistics.

[25]  Peter F. Christoffersen,et al.  Dynamic Dependence in Corporate Credit , 2013 .

[26]  Harry Joe,et al.  Composite Likelihood Methods , 2012 .

[27]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[28]  J. Wooldridge,et al.  A Capital Asset Pricing Model with Time-Varying Covariances , 1988, Journal of Political Economy.

[29]  Christian Gourieroux,et al.  Statistics and econometric models , 1995 .

[30]  Thomas H. McCurdy,et al.  Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions? , 2008 .

[31]  R. Nelsen.  An Introduction to Copulas , 1998 .

[32]  John M. Maheu,et al.  Modeling Realized Covariances and Returns , 2013 .

[33]  F. Diebold,et al.  Chapter 15 Volatility and Correlation Forecasting , 2006 .

[34]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[35]  D. Rivers,et al.  Model Selection Tests for Nonlinear Dynamic Models , 2002 .

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

[37]  N. Shephard.  Stochastic Volatility: Selected Readings , 2005 .

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

[39]  R. Engle,et al.  Multivariate Simultaneous Generalized ARCH , 1995, Econometric Theory.

[40]  GourierouxMonfort.  Statistics and Econometric Models, Volume 2 , 1996 .

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

[42]  Drew D. Creal,et al.  Generalized autoregressive score models with applications ∗ , 2010 .

[43]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .

[44]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .