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英文文献：Goodness-of-fit testing for fractional diffusions-分数扩散的拟合优度检验
英文文献作者：Mark Podolskij,Katrin Wasmuth
英文文献摘要：
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.
本文给出了平稳中心增量的高斯过程驱动的SDE波动函数的拟合优度检验方法。在相当弱的高斯过程假设下，我们提供了一个程序来检验未知的波动函数是否存在于给定的线性函数空间中。这个测试问题是非常重要的，因为在我们的模型中波动函数是不可识别的。基本的分数扩散假设是在固定的时间间隔上的高频观察，测试统计量是基于加权的功率变化。我们的测试统计数据与任何固定的选择是一致的。
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