Statistics of Lévy-driven Models

Levy 驱动模型的统计

• 批准号: 190212351
• 负责人: Professorin Dr. Vicky Fasen-Hartmann
• 金额: --
• 依托单位: Institut für Stochastik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/190212351?language=en
• 关键词: Statistics; vy; driven; Models

Time series models defined in continuous time are important for stochastic modelling in many areas of applications like e.g. finance, insurance, physics, signal processing and control. To obtain realistic marginal distributions and dynamics and to ensure a high mathematical tractability Lévy processes – a class of stochastic processes including, for instance, Brownian motion, Poisson processes and α-stable Lévy motions – are used as the random driving force. In this project we consider (multivariate) models which are of moving average type and especially the very important class of continuous-time autoregressive moving average (CARMA) processes. The aim is to considerably advance the understanding of their statistical and probabilistic properties and to develop a concise theory of statistical inference assuming that the processes are observed only at finitely many points in time. Thus, several estimators for stationary Lévy-driven moving average and CARMA processes are to be defined and analysed. Since often multivariate data sets are not stationary, but certain linear combinations are stationary, we investigate the definition of co-integration in a multivariate Lévy-driven CARMA framework and the related statistical inference. To improve the applicability of our estimators we study bootstrap methods.

在连续时间中定义的时间序列模型对于许多应用领域的随机建模非常重要，例如金融、保险、物理、信号处理和控制。为了获得真实的边际分布和动态，并确保高度的数学可跟踪性，将lsamvy过程——一类随机过程，例如布朗运动、泊松过程和α-稳定lsamvy运动——用作随机驱动力。在这个项目中，我们考虑（多变量）模型是移动平均类型，特别是非常重要的一类连续时间自回归移动平均（CARMA）过程。其目的是大大提高对其统计和概率性质的理解，并发展一种简明的统计推断理论，假设这些过程仅在有限多个时间点上被观察到。因此，将定义和分析固定的lsamv驱动的移动平均和CARMA过程的几个估计量。由于多元数据集通常是不平稳的，但某些线性组合是平稳的，我们研究了多元lsamv驱动的CARMA框架中协整的定义和相关的统计推断。为了提高估计器的适用性，我们研究了自举方法。

项目成果

Moment based estimation of supOU processes and a related stochastic volatility model

supOU 过程的基于矩的估计和相关的随机波动模型

• DOI: 10.1515/strm-2012-1152
• 发表时间: 2015
• 期刊: Statistics and Risk Modeling
• 影响因子: 1.5
• 作者: Stelzer;Tosstorff;Wittlinger
• 通讯作者: Wittlinger

Functional regular variation of Lévy-driven multivariate mixed moving average processes

Lévy 驱动的多元混合移动平均过程的函数正则变分

• DOI: 10.1007/s10687-012-0165-y
• 发表时间: 2013
• 期刊: Extremes
• 影响因子: 1.3
• 作者: Stelzer

Limit Theory for High Frequency Sampled MCARMA Models

高频采样 MCARMA 模型的极限理论

• DOI: 10.1239/aap/1409319563
• 发表时间: 2014
• 期刊: Advances in Applied Probability
• 影响因子: 1.2

Prediction of Lévy-driven CARMA processes

Lévy 驱动的 CARMA 过程的预测

• DOI: 10.1016/j.jeconom.2015.03.021
• 发表时间: 2015
• 期刊: Journal of Econometrics
• 影响因子: 6.3
• 作者: Brockwell;Lindner
• 通讯作者: Lindner

Dependence Estimation for High‐frequency Sampled Multivariate CARMA Models

高频采样多元 CARMA 模型的相关性估计

• DOI: 10.1111/sjos.12180
• 发表时间: 2016
• 期刊: Scandinavian Journal of Statistics
• 影响因子: 1