Small Sample Properties of Copula-GARCH Modelling: A Monte Carlo Study

Carluccio Bianchi (), Dean Fantazzini, Maria Elena De Giuli () and Mario Maggi ()
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Carluccio Bianchi: Department of Economics and Quantitative Methods, University of Pavia
Maria Elena De Giuli: Department of Economics and Quantitative Methods, University of Pavia
Mario Maggi: Department of Economics and Quantitative Methods, University of Pavia

No 93, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: Copula-GARCH models have been recently proposed in the financial literature as a statistical tool to build 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 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: Copulas; Copula-GARCH models; Maximum Likelihood; Simulation; Small Sample Properties. (search for similar items in EconPapers)
JEL-codes: C15 C32 C51 C63 (search for similar items in EconPapers)
Pages: 72 pages
Date: 2009-02
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http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q093.pdf (application/pdf)

Related works:
Journal Article: Small sample properties of copula-GARCH modelling: a Monte Carlo study (2011)
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