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Wishart Processes in Statistics and Econometrics: Theory and Applications

统计和计量经济学中的威沙特过程：理论与应用

基本信息

批准号：
196283488
负责人：
Privatdozent Dr. Taras Bodnar
金额：
--
依托单位：
Institut für Mathematik
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 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/196283488?language=en
关键词：
Wishart Processes Statistics Econometrics Theory

项目摘要

The purpose of this project is to make a series of theoretical and practical contributions in two major fields. The first field deals with statistical properties of the Wishart distribution and its several extensions. First, we analyze the Wishart distribution not isolated, but in a combination with a Gaussian vector. This fact is motivated by applications in discriminant analysis and portfolio theory, where the key quantities are given by a product of inverse Wishart matrix and a Gaussian vector. Second, in the light of the increasing importance of asymmetric distributions, we extend the concept of the Wishart matrices to matrices obtained from truncated and skewed Gaussian vectors. Third, we use the results to extend the paper of Bodnar et al. (2009) by developing statistical monitoring procedures for new distribution classes. The second field of contribution is econometrically oriented. Recent econometric developments show an increasing interest in time-series models for Wishart processes. Within the project we will extend the results of Gourieroux et al. (2009) and Chiriac and Voev (2010) to develop the theory of autoregressive (inverse, singular) Wishart processes. This type of the models is particularly important for multivariate modelling of the volatility dynamics and realized volatilities based on high-frequency data. Furthermore, a new multivariate class of stochastic volatility processes will be suggested which relies on the square root of the autoregressive Wishart process. This is a new and interesting alternative to current multivariate GARCH models.

该项目的目的是在两个主要领域做出一系列的理论和实践贡献。第一个字段处理Wishart分布及其几个扩展的统计特性。首先，我们分析了Wishart分布，不是孤立的，而是与高斯向量的组合。这一事实是由判别分析和投资组合理论中的应用所激发的，其中关键量由逆Wishart矩阵和高斯向量的乘积给出。其次，鉴于不对称分布的重要性日益增加，我们将Wishart矩阵的概念扩展到由截断和偏斜高斯向量得到的矩阵。第三，我们通过开发新分布类别的统计监测程序，利用结果扩展了Bodnar等人（2009）的论文。第二个贡献领域是计量经济学导向的。最近的计量经济学发展表明，人们对Wishart过程的时间序列模型越来越感兴趣。在该项目中，我们将扩展Gourieroux等人（2009）和Chiriac和Voev（2010）的结果，以发展自回归（逆，奇异）Wishart过程理论。这类模型对于波动性动态和基于高频数据的已实现波动性的多变量建模尤为重要。此外，还提出了一种新的多元随机波动过程，它依赖于自回归Wishart过程的平方根。这是当前多元GARCH模型的一个新的和有趣的替代方案。