Small sample properties of copula-GARCH modelling: a Monte Carlo study

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Abstract:

Copula-GARCH models have been recently proposed in the financial literature as a statistical tool to deal with flexible multivariate distributions. Our extensive simulation studies investigate the small sample properties of these models and examine how misspecification in the marginals may affect the estimation of the dependence function represented by the copula. We show that the use of Normal marginals when the true Data Generating Process (DGP) is leptokurtic or asymmetric, produces negatively biased estimates of the Normal copula correlations. A striking result is that these biases reach their highest value when correlations are strongly negative, and viceversa. This result remains unchanged with both positively skewed and negatively skewed data, while no biases are found if the variables are uncorrelated. Besides, the effect of marginals asymmetry on correlations is smaller than that of leptokurtosis. We finally analyse the performance of these models in terms of numerical convergence and positive definiteness of the estimated copula correlation matrix.

Keywords: C15; C32; C51; C63; copula-GARCH models; copulas; maximum likelihood; simulation; small sample properties

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/09603107.2011.587770

Affiliations: 1: Department of Economics and Quantitative Methods,University of Pavia, University of Pavia, Via S. Felice, 5Pavia 27100, Italy 2: Moscow School of Economics, 1, Building 61, Leninskie Gory, M.V. Lomonosov MSU 119992Moscow, Russia

Publication date: November 1, 2011

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