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.
OriginalsprogEngelsk
TidsskriftStatistical Inference for Stochastic Processes
Vol/bind16
Nummer2
Sider (fra-til)147-159
Antal sider13
ISSN1387-0874
DOI
StatusUdgivet - 1 jul. 2013

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