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Goodness-of-fit testing for fractional diffusions

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  • Mark Podolskij

    ()
    (Heidelberg University and CREATES)

  • Katrin Wasmuth

    ()
    (Heidelberg University)

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    Abstract

    This paper presents a goodness-of-fit test for the volatility function of a SDE driven by a Gaussian process with stationary and centered increments. Under rather weak assumptions on the Gaussian process, we provide a procedure for testing whether the unknown volatility function lies in a given linear functional space or not. This testing problem is highly non-trivial, because the volatility function is not identifiable in our model. The underlying fractional diffusion is assumed to be observed at high frequency on a fixed time interval and the test statistic is based on weighted power variations. Our test statistic is consistent against any fixed alternative.

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    File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_12.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 2012-12.

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    Length: 13
    Date of creation: 16 Apr 2012
    Date of revision:
    Handle: RePEc:aah:create:2012-12

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

    Related research

    Keywords: central limit theorem; goodness-of-fit tests; high frequency observations; fractional diffusions; stable convergence.;

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    1. Vetter, Mathias & Podolskij, Mark & Dette, Holger, 2004. "Estimation of integrated volatility in continuous time financial models with applications to goodness-of-fit testing," Technical Reports 2004,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, School of Economics and Management, University of Aarhus.
    3. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Limit theorems for functionals of higher order differences of Brownian semi-stationary processes," CREATES Research Papers 2009-60, School of Economics and Management, University of Aarhus.
    4. Barndorff-Nielsen, Ole E. & Corcuera, José Manuel & Podolskij, Mark, 2009. "Power variation for Gaussian processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1845-1865, June.
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