Kernel estimation for Lévy driven stochastic convolutions

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2021-08-11 DOI:10.1515/strm-2021-0007

F. Comte, V. Genon-Catalot

引用次数: 0

Abstract

Abstract We consider a Lévy driven stochastic convolution, also called continuous time Lévy driven moving average model X⁢(t)=∫0ta⁢(t-s)⁢dZ⁢(s)X(t)=\int_{0}^{t}a(t-s)\,dZ(s), where 𝑍 is a Lévy martingale and the kernel a(.)a(\,{.}\,) a deterministic function square integrable on R+\mathbb{R}^{+}. Given 𝑁 i.i.d. continuous time observations (Xi⁢(t))t∈[0,T](X_{i}(t))_{t\in[0,T]}, i=1,…,Ni=1,\dots,N, distributed like (X⁢(t))t∈[0,T](X(t))_{t\in[0,T]}, we propose two types of nonparametric projection estimators of a2a^{2} under different sets of assumptions. We bound the L2\mathbb{L}^{2}-risk of the estimators and propose a data driven procedure to select the dimension of the projection space, illustrated by a short simulation study.

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lsamvy驱动随机卷积的核估计

我们考虑一个l驱动随机卷积，也称为连续时间l驱动移动平均模型X²(t)=∫0ta²(t-s)²dZ²(s)X(t)=\int＿{0}＾{t}a(t-s)\，dZ(s)，其中𝑍是一个λ鞅，核a(.)a(\，{．}\，)在R+上平方可积的确定性函数\mathbb{R}＾{+}。{I}(1){t\in[0,T]}， i=1，…，Ni=1，\dots，N，分布于(X¹(t))t∈[0,t](X(t))＿{t\in[0,T]}，我们提出了a2a^的两类非参数投影估计量{2} 在不同的假设下。我们限定了L2\mathbb{L}＾{2}提出了一种数据驱动的方法来选择投影空间的维数，并通过一个简短的仿真研究加以说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.