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

  • Jean Jacod

    ()

    (University Paris VI)

  • Mark Podolskij

    ()

    (Heidelberg University and CREATES)

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    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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    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
    Contact details of provider: Web page: http://www.econ.au.dk/afn/

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    1. Robin, J.M. & Smith, R.J., 1995. "Tests of Rank," Cambridge Working Papers in Economics 9521, Faculty of Economics, University of Cambridge.
    2. Mark Podolskij & Mathieu Rosenbaum, 2011. "Testing the local volatility assumption: a statistical approach," CREATES Research Papers 2011-04, School of Economics and Management, University of Aarhus.
    3. 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, vol. 31(3), pages 417-429.
    4. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
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