Goodness-of-fit testing for fractional diffusions
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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- 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.
- 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.
- 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.
- Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2007. "Power variation for Gaussian processes with stationary increments," CREATES Research Papers 2007-42, Department of Economics and Business Economics, Aarhus University.
- Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij & Jeannette H.C. Woerner, 2008. "Bipower variation for Gaussian processes with stationary increments," CREATES Research Papers 2008-21, Department of Economics and Business Economics, Aarhus University.
- 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.
- 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.
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