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A test for the rank of the volatility process: the random perturbation approach

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  • Jean Jacod

    ()
    (University Paris VI)

  • Mark Podolskij

    ()
    (Heidelberg University and CREATES)

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    Abstract

    In this paper we present a test for the maximal rank of the matrix-valued volatility process in the continuous Itô semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Itô semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.

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    File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_57.pdf
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    Bibliographic Info

    Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-57.

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    Length: 30
    Date of creation: 14 Dec 2012
    Date of revision:
    Handle: RePEc:aah:create:2012-57

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    Web page: http://www.econ.au.dk/afn/

    Related research

    Keywords: central limit theorem; high frequency data; homoscedasticity testing; Itô semimartingales; rank estimation; stable convergence.;

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    1. Robin, J.M. & Smith, R.J., 1995. "Tests of Rank," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9521, Faculty of Economics, University of Cambridge.
    2. Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, Springer, vol. 8(1), pages 31-48, February.
    3. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 118(4), pages 517-559, April.
    4. Susanne Ditlevsen & Michael Sørensen, 2004. "Inference for Observations of Integrated Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 417-429.
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