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

Applied Financial Economics, Forthcoming

Posted: 20 Sep 2011 Last revised: 2 Oct 2017

See all articles by Carluccio Bianchi

Carluccio Bianchi

University of Pavia - Department of Economics and Management

Maria Elena De Giuli

University of Pavia - Department of Political Economy and Quantitative Methods

Dean Fantazzini

Moscow School of Economics, Moscow State University; National Research University Higher School of Economics

Mario Maggi

University of Pavia - Department of Economics and Management; University of Pavia - Department of Economics and Management

Date Written: September 18, 2011

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: Copulas, Copula-GARCH models, Maximum Likelihood, Simulation, Small Sample Properties

JEL Classification: C15, C32, C51, C63

Suggested Citation

Bianchi, Carluccio and De Giuli, Maria Elena and Fantazzini, Dean and Maggi, Mario, Small Sample Properties of Copula-GARCH Modelling: A Monte Carlo Study (September 18, 2011). Applied Financial Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1929975

Carluccio Bianchi

University of Pavia - Department of Economics and Management ( email )

Strada Nuova, 65
Pavia, 27100
Italy
+390382986212 (Phone)
+390382304226 (Fax)

HOME PAGE: http://economia.unipv.it/pagp/pagine_personali/cbianchi/bianchi.htm

Maria Elena De Giuli

University of Pavia - Department of Political Economy and Quantitative Methods ( email )

27100 Pavia
Italy

Dean Fantazzini (Contact Author)

Moscow School of Economics, Moscow State University ( email )

GSP-2, Leninskie Gory
Moscow, 119992
Russia
+7 495 5105256 (Phone)
+7 495 5105267 (Fax)

HOME PAGE: https://sites.google.com/site/deanfantazzini/

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

HOME PAGE: http://www.hse.ru/org/persons/11532644

Mario Maggi

University of Pavia - Department of Economics and Management ( email )

Via San Felice, 5
Pavia, PV 27100
Italy

HOME PAGE: http://economia.unipv.it/pagp/pagine_personali/maggma/moreinfo.htm

University of Pavia - Department of Economics and Management ( email )

Strada Nuova, 65
Pavia, 27100
Italy

HOME PAGE: http://economia.unipv.it/pagp/pagine_personali/maggma/moreinfo.htm

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