Goodness-of-fit testing for fractional diffusions

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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.
Original languageEnglish
JournalStatistical Inference for Stochastic Processes
Volume16
Issue2
Pages (from-to)147-159
Number of pages13
ISSN1387-0874
DOIs
Publication statusPublished - 1 Jul 2013

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