In this article we present a parametric estimation method for certain multiparameter heavy-tailed Lévy-driven moving averages. The theory relies on recent multivariate central limit theorems obtained via Malliavin calculus on Poisson spaces. Our minimal contrast approach is related to previous papers, 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 multiparametric 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.

中文翻译：

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重尾移动平均线的多维参数估计

在本文中，我们提出了一种用于某些多参数重尾 Lévy 驱动移动平均线的参数估计方法。该理论依赖于最近通过泊松空间上的 Malliavin 演算获得的多元中心极限定理。我们的最小对比方法与之前的论文有关，其中提出使用边际经验特征函数来估计核函数的一维参数和驾驶 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，该框架特别包括线性分数稳定运动、稳定的 Ornstein-Uhlenbeck 过程、某些 CARMA(2, 1) 模型和具有周期分量的 Ornstein-Uhlenbeck 过程的重要示例。其他型号。我们提出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，以揭示我们方法的有限样本性能。