论文标题
使用高频数据估算混合分数稳定过程
Estimation of mixed fractional stable processes using high-frequency data
论文作者
论文摘要
线性分数稳定运动概括了两种突出的随机过程，即稳定的Lévy过程和分数Brownian运动。因此，可以将其视为连续时间模型的基本构建块。我们研究了由独立线性分数稳定运动叠加组成的风格化模型，我们的重点是模型的参数估计。采用估计方程方法，我们为整个参数构造估计器，并在高频制度中得出其渐近正态性。对于两个显着的特殊情况，一致性的条件是鲜明的：（i）对于莱维过程，即估计连续的blumenthal-getoor指数，以及（ii）Cheridito引入的混合分数布朗尼运动。在其余情况下，我们的结果揭示了赫斯特参数与稳定指数之间的微妙相互作用。我们的渐近理论基于多尺度移动平均过程的新限制定理。
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable Lévy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time models. We study a stylized model consisting of a superposition of independent linear fractional stable motions and our focus is on parameter estimation of the model. Applying an estimating equations approach, we construct estimators for the whole set of parameters and derive their asymptotic normality in a high-frequency regime. The conditions for consistency turn out to be sharp for two prominent special cases: (i) for Lévy processes, i.e. for the estimation of the successive Blumenthal-Getoor indices, and (ii) for the mixed fractional Brownian motion introduced by Cheridito. In the remaining cases, our results reveal a delicate interplay between the Hurst parameters and the indices of stability. Our asymptotic theory is based on new limit theorems for multiscale moving average processes.
