论文标题
重尾移动平均值的多维参数估计
Multi-dimensional parameter estimation of heavy-tailed moving averages
论文作者
论文摘要
在本文中，我们提出了一种参数估计方法，用于某些多参数重尾Lévy-Lévy驱动的移动平均值。该理论依赖于[3]中通过泊松空间上通过malliavin conculus获得的最新多元中心极限定理。我们的最小对比方法与论文[14，15]有关，该论文提出使用边缘经验特征函数来估计内核函数的一维参数和驱动Lévy运动的稳定性指数。我们扩展了他们的工作，以允许一个多参数框架，尤其包括线性分数稳定运动的重要例子，稳定的Ornstein-Uhlenbeck过程，某些Carma（2，1）模型和Ornstein-Uhlenbeck过程，以及其他模型中有周期性的组件。我们介绍了最小对比度估计量的一致性和相关的中心极限定理。此外，我们展示了数值分析，以揭示方法的有限样本性能。
In this paper we present a parametric estimation method for certain multi-parameter heavy-tailed Lévy-driven moving averages. The theory relies on recent multivariate central limit theorems obtained in [3] via Malliavin calculus on Poisson spaces. Our minimal contrast approach is related to the papers [14, 15], which propose to use the marginal empirical characteristic function to estimate the one-dimensional parameter of the kernel function and the stability index of the driving Lévy motion. We extend their work to allow for a multi-parametric framework that in particular includes the important examples of the linear fractional stable motion, the stable Ornstein-Uhlenbeck process, certain CARMA(2, 1) models and Ornstein-Uhlenbeck processes with a periodic component among other models. We present both the consistency and the associated central limit theorem of the minimal contrast estimator. Furthermore, we demonstrate numerical analysis to uncover the finite sample performance of our method.
