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Comparing Correlation Matrix Estimators Via Kullback-Leibler Divergence

20 Pages Posted: 2 Dec 2011  

Vanessa Mattiussi

City University London - Department of Economics

Michele Tumminello

University of Palermo; Carnegie Mellon University - Department of Social and Decision Sciences

Giulia Iori

City University London - Department of Economics

Rosario N. Mantegna

University of Palermo

Date Written: November 30, 2011

Abstract

We use a self-averaging measure called Kullback-Leibler divergence to evaluate the performance of four different correlation estimators: Fourier, Pearson, Maximum Likelihood and Hayashi-Yoshida estimator. The study uses simulated transaction prices for a large number of stocks and different data generating mechanisms, including synchronous and non-synchronous transactions, homogeneous and heterogeneous inter-transaction time. Different distributions of stock returns, i.e. multivariate Normal and multivariate Student's t-distribution, are also considered. We show that Fourier and Pearson estimators are equivalent proxies of the `true' correlation matrix within all the settings under analysis, and that both methods are outperformed by the Maximum Likelihood estimator when prices are synchronously sampled and price fluctuations follow a multivariate Student's t-distribution. Finally, we suggest to solve the singularity problem affecting the Hayashi-Yoshida estimator by shrinking the correlation matrix towards either Pearson or Fourier matrices, and provide evidence that the resulting combination leads to an improved estimator with respect to its single components.

Keywords: Correlation estimation, Pearson estimator, Fourier estimator, Hayashi-Yoshida estimator, Kullback-Leibler divergence

JEL Classification: C13, G19

Suggested Citation

Mattiussi, Vanessa and Tumminello, Michele and Iori, Giulia and Mantegna, Rosario N., Comparing Correlation Matrix Estimators Via Kullback-Leibler Divergence (November 30, 2011). Available at SSRN: https://ssrn.com/abstract=1966714 or http://dx.doi.org/10.2139/ssrn.1966714

Vanessa Mattiussi

City University London - Department of Economics ( email )

Northampton Square
London, EC1V 0HB
United Kingdom

Michele Tumminello

University of Palermo ( email )

Viale delle Scienza
Palermo, Palermo 90128
Italy

Carnegie Mellon University - Department of Social and Decision Sciences ( email )

Pittsburgh, PA 15213-3890
United States

Giulia Iori

City University London - Department of Economics ( email )

Northampton Square
London, EC1V 0HB
United Kingdom

Rosario Nunzio Mantegna (Contact Author)

University of Palermo ( email )

Dipartimento di Fisica
Viale delle Scienze, Edificio 18
Palermo, PA I-90128
Italy
+3909123899074 (Phone)
+3909123860815 (Fax)

HOME PAGE: http://ocs.unipa.it/Site/Rosario_Nunzio_Mantegna.html

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