A Range-Based Test for the Parametric Form of the Volatility in Diffusion M...

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英文文献：A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models-扩散模型中波动的参数形式的基于范围的检验
英文文献作者：Mark Podolskij,Daniel Ziggel
英文文献摘要：
We propose a new test for the parametric form of the volatility function in continuous time diffusion models of the type dXt = a(t;Xt)dt + _(t;Xt)dWt. Our approach involves a range-based estimation of the integrated volatility and the integrated quarticity, which are used to construct the test statistic. Under rather weak assumptions on the drift and volatility we prove weak convergence of the test statistic to a centered mixed Gaussian distribution. As a consequence we obtain a test, which is consistent for any fixed alternative. We also provide a test for neighborhood hypotheses. Moreover, we present a parametric bootstrap procedure which provides a better approximation of the distribution of the test statistic. Finally, it is demonstrated by means of Monte Carlo study that the range-based test is more powerful than the return-based test when comparing at the same sampling frequency.

摘要对连续时间扩散模型中dXt = a(t;Xt)dt + _(t;Xt)dWt的波动函数的参数形式提出了一种新的检验方法。我们的方法涉及到基于范围的综合波动率和综合质量的估计，用于构造检验统计量。在相当弱的漂移和波动假设下，证明了检验统计量对集中的混合高斯分布的弱收敛性。因此，我们得到了一个测试，它对任何固定的选择都是一致的。我们还为邻域假设提供了一个测试。此外，我们提出了一个参数自举程序，它提供了一个更好的估计检验统计量的分布。最后，通过蒙特卡罗研究表明，在相同的采样频率下，基于距离的检验比基于回归的检验更有效。

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