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Modeling Time-Varying Dependencies Between Positive-Valued High-Frequency Time Series

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Copulae in Mathematical and Quantitative Finance

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 213))

Abstract

Multiplicative error models (MEM) became a standard tool for modeling conditional durations of intraday transactions, realized volatilities, and trading volumes. The parametric estimation of the corresponding multivariate model, the so-called vector MEM (VMEM), requires a specification of the joint error term distribution, which is due to the lack of multivariate distribution functions on \(\mathbb{R}_{+}^{d}\) defined via a copula. Maximum likelihood estimation is based on the assumption of constant copula parameters and therefore leads to invalid inference if the dependence exhibits time variations or structural breaks. Hence, we suggest to test for time-varying dependence by calibrating a time-varying copula model and to re-estimate the VMEM based on identified intervals of homogenous dependence. This paper summarizes the important aspects of (V)MEM, its estimation, and a sequential test for changes in the dependence structure. The techniques are applied in an empirical example.

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Acknowledgments

The financial support from the Deutsche Forschungsgemeinschaft via SFB 649 Ökonomisches Risiko, Humboldt-Universität zu Berlin is gratefully acknowledged.

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Authors and Affiliations

  1. School of Business and Economics, Humboldt-Universität zu Berlin, Berlin, Germany

    Nikolaus Hautsch, Ostap Okhrin & Alexander Ristig

Authors
  1. Nikolaus Hautsch
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  2. Ostap Okhrin
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  3. Alexander Ristig
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Corresponding author

Correspondence to Alexander Ristig .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, Warszawa, 02097, Poland

    Piotr Jaworski

  2. School of Economics and Management, Free University of Bozen-Bolzano, Piazza Università 1, Bozen, 39100, Italy

    Fabrizio Durante

  3. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

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Hautsch, N., Okhrin, O., Ristig, A. (2013). Modeling Time-Varying Dependencies Between Positive-Valued High-Frequency Time Series. In: Jaworski, P., Durante, F., Härdle, W. (eds) Copulae in Mathematical and Quantitative Finance. Lecture Notes in Statistics(), vol 213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35407-6_6

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