Ranking Multivariate GARCH Models by Problem Dimension : An Empirical Evaluation *

In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. Recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC, Exponentially Weighted Moving Average, and covariance shrinking, using historical data of 89 US equities. Our methods follow part of the approach described in Patton and Sheppard (2009), and the paper contributes to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem.

[1]  M. Rothschild,et al.  Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills , 1988 .

[2]  T. Bollerslev,et al.  Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model , 1990 .

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

[4]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[5]  K. West,et al.  Asymptotic Inference about Predictive Ability , 1996 .

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

[7]  David I. Harvey.  The evaluation of economic forecasts , 1997 .

[8]  Thierry Jeantheau,et al.  STRONG CONSISTENCY OF ESTIMATORS FOR MULTIVARIATE ARCH MODELS , 1998, Econometric Theory.

[9]  Y. Tse,et al.  A Multivariate GARCH Model with Time-Varying Correlations , 2000 .

[10]  H. White,et al.  A Reality Check for Data Snooping , 2000 .

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

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

[13]  Zhuanxin Ding,et al.  Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing , 2001 .

[14]  Roy van der Weide,et al.  GO-GARCH: a multivariate generalized orthogonal GARCH model , 2002 .

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

[16]  Asger Lunde,et al.  Choosing the Best Volatility Models: The Model Confidence Set Approach , 2003 .

[17]  Miguel A. Ferreira,et al.  Evaluating Interest Rate Covariance Models within a Value-at-Risk Framework , 2004 .

[18]  Christian M. Hafner,et al.  Analytical quasi maximum likelihood inference in multivariate volatility models , 2003 .

[19]  Olivier Ledoit,et al.  Honey, I Shrunk the Sample Covariance Matrix , 2003 .

[20]  Offer Lieberman,et al.  Asymptotic theory for multivariate GARCH processes , 2003 .

[21]  Michael McAleer,et al.  ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL , 2003, Econometric Theory.

[22]  Ioannis D. Vrontos,et al.  A Full-Factor Multivariate GARCH Model , 2003 .

[23]  Pierre Giot,et al.  Market Models: A Guide to Financial Data Analysis , 2003 .

[24]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

[25]  Olivier Ledoit,et al.  Improved estimation of the covariance matrix of stock returns with an application to portfolio selection , 2003 .

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

[27]  P. Hansen,et al.  Consistent Ranking of Volatility Models , 2006 .

[28]  P. Hansen,et al.  A Forecast Comparison of Volatility Models: Does Anything Beat a Garch(1,1)? , 2004 .

[29]  Pentti Saikkonen,et al.  A Multivariate Generalized Orthogonal Factor GARCH Model , 2007 .

[30]  M. McAleer.  Automated Inference and Learning in Modelling Financial Volatility * , 2004 .

[31]  P. Hansen.  A Test for Superior Predictive Ability , 2005 .

[32]  Riccardo Colacito,et al.  Testing and Valuing Dynamic Correlations for Asset Allocation , 2005 .

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

[34]  Monica Billio,et al.  Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation , 2006 .

[35]  Michael McAleer,et al.  Realized Volatility: A Review , 2008 .

[36]  M. McAleer,et al.  Multivariate Stochastic Volatility: A Review , 2006 .

[37]  Gianni Amisano,et al.  Comparing Density Forecasts via Weighted Likelihood Ratio Tests , 2007 .

[38]  R. Engle,et al.  Evaluating the Specification of Covariance Models for Large Portfolios , 2007 .

[39]  Michael McAleer,et al.  GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION , 2008, Econometric Theory.

[40]  M. McAleer,et al.  Scalar BEKK and indirect DCC , 2008 .

[41]  N. Shephard,et al.  Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading , 2010 .

[42]  Timo Terasvirta,et al.  Multivariate GARCH Models , 2008 .

[43]  P. Paruolo,et al.  Structured Multivariate Volatility Models , 2008 .

[44]  M. McAleer,et al.  Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models , 2009 .

[45]  G. Zumbach.  Empirical properties of large covariance matrices , 2009, 0903.1525.

[46]  Kevin Sheppard,et al.  Evaluating Volatility and Correlation Forecasts , 2009 .

[47]  Valeri Voev.  On the Economic Evaluation of Volatility Forecasts , 2009 .

[48]  R. Becker,et al.  Evaluating multivariate volatility forecasts , 2009 .

[49]  G. Storti,et al.  Combination of multivariate volatility forecasts , 2009 .

[50]  Victor DeMiguel,et al.  Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? , 2009 .

[51]  S. Chib,et al.  Multivariate stochastic volatility , 2009 .

[52]  Christian M. Hafner,et al.  On asymptotic theory for multivariate GARCH models , 2009, J. Multivar. Anal..

[53]  Michael McAleer,et al.  Block Structure Multivariate Stochastic Volatility Models , 2009 .

[54]  P. Franses,et al.  A Generalized Dynamic Conditional Correlation Model: Simulation and Application to Many Assets , 2009 .

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

[56]  J. Zakoian,et al.  QML estimation of a class of multivariate GARCH models without moment conditions on the observed process , 2010 .

[57]  S. Laurent,et al.  On the Forecasting Accuracy of Multivariate GARCH Models , 2010 .

[58]  R. Engle,et al.  Dynamic Equicorrelation , 2011 .

[59]  Christian M. Hafner,et al.  On the estimation of dynamic conditional correlation models , 2012, Comput. Stat. Data Anal..

[60]  A. Hurn,et al.  On the efficacy of techniques for evaluating multivariate volatility forecasts , 2012 .

[61]  K. West,et al.  FORECAST EVALUATION , 2022 .