Nuisance parameters, composite likelihoods and a panel of GARCH models

We investigate the properties of the composite likelihood (CL) method for (T A—N_T ) GARCH panels. The defining feature of a GARCH panel with time series length T is that, while nuisance parameters are allowed to vary across N_T series, other parameters of interest are assumed to be common. CL pools information across the panel instead of using information available in a single series only. Simulations and empirical analysis illustrate that in reasonably large T CL performs well. However, due to the estimation error introduced through nuisance parameter estimation, CL is subject to the “incidental parameter†problem for small T .

[1]  R. Engle.  Dynamic Conditional Correlation : A Simple Class of Multivariate GARCH Models , 2000 .

[2]  Luca Benzoni,et al.  Realized Volatility , 2008 .

[3]  T. Lancaster.  The incidental parameter problem since 1948 , 2000 .

[4]  N. Shephard,et al.  Econometric analysis of realised volatility and its use in estimating stochastic volatility models , 2000 .

[5]  Timo Teräsvirta,et al.  Multivariate GARCH models To appear in T. G. Andersen, R. A. Davis, J.-P. Kreiss and T. Mikosch, eds. Handbook of Financial Time Series. New York: Springer. , 2008 .

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

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

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

[9]  B. Lindsay.  Using Empirical Partially Bayes Inference for Increased Efficiency , 1985 .

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

[11]  C. Varin.  On composite marginal likelihoods , 2008 .

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

[13]  Luc Bauwens,et al.  Bayesian Clustering of Many Garch Models , 2003 .

[14]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

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

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

[17]  James J. Heckman,et al.  Handbook of Econometrics, Volume 7A , 2001 .

[18]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[19]  Spain,et al.  PANEL DATA MODELS : SOME RECENT DEVELOPMENTS * , 2004 .

[20]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

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

[22]  Andrew J. Patton,et al.  Volatility Forecast Evaluation and Comparison Using Imperfect Volatility Proxies , 2005 .

[23]  Jennifer L. Castle,et al.  The Methodology and Practice of Econometrics , 2009 .

[24]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

[25]  Nicola Sartori,et al.  Modified profile likelihoods in models with stratum nuisance parameters , 2003 .

[26]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[27]  Empirical Bayes and conditional inference with many nuisance parameters , 1992 .

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

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

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

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

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

[33]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

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