In this paper we present a parametric estimation method for certain multi-parameter heavy-tailed L\'evy-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 L\'evy 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.

翻译：在本文中,我们为某些多参数重尾L\'evy驱动的移动平均值提出了一个参数估计方法。该理论依赖于最近在Poisson空间上通过Malliavin calculus获得的[3]年多变中央参数。我们最小的对比方法与论文[14, 15]有关,这些论文提议使用边际经验特征功能来估计内核函数的一维参数和驱动L\'evy运动的稳定性指数。我们扩大了它们的工作,以便建立一个多参数框架,其中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Ornstein-Uhlenbeck过程的重要例子,并附有其他模型中的定期组成部分。我们提出了最小对比测算器的一致性和相关的中心限制。此外,我们展示了数字分析,以发现我们方法的有限样品性能。