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Goodness-of-fit testing for fractional diffusions

Author

Listed:
  • Mark Podolskij

    () (Heidelberg University and CREATES)

  • Katrin Wasmuth

    () (Heidelberg University)

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.

Suggested Citation

  • Mark Podolskij & Katrin Wasmuth, 2012. "Goodness-of-fit testing for fractional diffusions," CREATES Research Papers 2012-12, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-12
    as

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    File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_12.pdf
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    References listed on IDEAS

    as
    1. 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, Department of Economics and Business Economics, Aarhus University.
    2. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, Department of Economics and Business Economics, Aarhus University.
    3. 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.
    4. Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

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

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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