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Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity

58 Pages Posted: 24 Jan 2014 Last revised: 14 Nov 2016

Kris Boudt

Vrije Universiteit Brussel (VUB); VU University Amsterdam

Sébastien Laurent

French National Center for Scientific Research (CNRS) - Research Group in Quantitative Saving (GREQAM)

Asger Lunde

University of Aarhus - School of Economics and Management; CREATES

Rogier Quaedvlieg

Erasmus University Rotterdam (EUR) - Department of Business Economics

Orimar Sauri

University of Aarhus - School of Business and Social Sciences

Date Written: May 10, 2016

Abstract

An estimator of the ex-post covariation of log-prices under asynchronicity and microstructure noise is proposed. It uses the Cholesky factorization of the covariance matrix in order to exploit the heterogeneity in trading intensities to estimate the different parameters sequentially with as many observations as possible. The estimator is positive semidefinite by construction. We derive asymptotic results and confirm their good finite sample properties by means of a Monte Carlo simulation. In the application we forecast portfolio Value-at-Risk and sector risk exposures for a portfolio of 52 stocks. We find that the dynamic models utilizing the proposed high-frequency estimator provide statistically and economically superior forecasts.

Keywords: Cholesky decomposition, Integrated covariance, Positive semidefinite

JEL Classification: C10, C58

Suggested Citation

Boudt, Kris and Laurent, Sébastien and Lunde, Asger and Quaedvlieg, Rogier and Sauri, Orimar, Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity (May 10, 2016). Journal of Econometrics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2383871 or http://dx.doi.org/10.2139/ssrn.2383871

Kris Boudt

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Sébastien Laurent

French National Center for Scientific Research (CNRS) - Research Group in Quantitative Saving (GREQAM) ( email )

Centre de la Vieille Charité
2, rue de la Charité
Marseille, 13002
France

Asger Lunde

University of Aarhus - School of Economics and Management ( email )

Aarhus
Denmark

CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Rogier Quaedvlieg (Contact Author)

Erasmus University Rotterdam (EUR) - Department of Business Economics ( email )

Netherlands

Orimar Sauri

University of Aarhus - School of Business and Social Sciences ( email )

Nordre Ringgade 1
Aarhus C, DK-8000
Denmark

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