论文标题
扩散Copulas：识别和估计
Diffusion Copulas: Identification and Estimation
论文作者
论文摘要
我们提出了一种新的半参数方法，用于建模非线性单变量扩散，其中观察到的过程是基础参数扩散（UPD）的非参数转换。这种建模策略产生了具有参数动态Copulas和非参数边缘分布的一般半参数Markov扩散模型。我们为识别UPD参数以及离散样本的未知转换提供了原始条件。开发了基于参数和非参数组件的可能性估计量，我们分析了这些成分的渐近性能。还提出了基于内核的漂移和扩散估计量，并显示出在大型样本中正态分布。一项模拟研究调查了在对美国短期利率建模的背景下，我们的估计量的有限样本性能。我们还提出了对CBOE波动率指数数据进行建模的简单应用。
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations from discrete samples. Likelihood-based estimators of both parametric and nonparametric components are developed and we analyze the asymptotic properties of these. Kernel-based drift and diffusion estimators are also proposed and shown to be normally distributed in large samples. A simulation study investigates the finite sample performance of our estimators in the context of modelling US short-term interest rates. We also present a simple application of the proposed method for modelling the CBOE volatility index data.
