Non-Gaussian Time Series and Nonlinear Dependence in Finance Markets, 2016

Two key statistical features of finance markets are non-linearity and Non-Gaussianity. Between 2011 and 2012, Dag Tjøstheim coordinated the research of the project "Non-Guassian Time Series and Nonlinear Dependence", financed by The Finance Market Fund. The activity of the project was spread over three sub-projects, namely i) Local Gaussian correlation, ii) Nonlinear cointegration and iii) Integer-valued time series. In the referee report for the project it was pointed out that i) was most relevant for financial markets. Therefore the focus was directed towards this in the project "Non-Gaussian Time Series and Nonlinear Dependence in Finance Markets, 2016", for which metadata is presented here. Topics from i) that received attention were multivariate heavy tail dependence, multivariate extreme events, and multivariate portfolio analysis and risk. In addition we considered nonlinear cointegration theory using local Gaussian correlation, this combining i) and ii). Finally we explored the relationships to multiple copula theory, in particular the vine theory. All of this was relevant for the statistical analysis of financial markets.

金融市场的两大核心统计特征为非线性性与非高斯性（Non-Gaussianity）。2011至2012年间，达格·约斯泰姆（Dag Tjøstheim）牵头了由金融市场基金资助的"非高斯时间序列与非线性依赖"研究项目。该项目的研究内容涵盖三个子课题，分别为：i）局部高斯相关（Local Gaussian correlation），ii）非线性协整（Nonlinear cointegration），以及iii）整数值时间序列（Integer-valued time series）。在该项目的评审报告中指出，子课题i）与金融市场的关联性最强。因此在2016年启动的题为"金融市场中的非高斯时间序列与非线性依赖"的项目中，研究重心便转向了该子课题，本文即呈现该项目的元数据。该子课题i）的研究重点涵盖多元厚尾依赖、多元极端事件、多元投资组合分析与风险管控。此外，我们结合子课题i）与ii），探索了基于局部高斯相关的非线性协整理论。最后，我们还探讨了其与多元Copula理论（Copula theory），尤其是藤Copula理论（vine theory）的关联。上述所有研究内容均服务于金融市场的统计分析工作。