Cross-Sectional and Temporal Dependence in Complex Data

理解数据序列的时间随机性是许多研究领域的核心，无论是学术还是行业。例如，金融行业对从大型数据集中推断信息特别感兴趣，从而发现通过识别信号揭示的任何模式。还有一个额外的维度：不仅需要在统计分析和随机时间序列的数学（时间分析）方面取得进步，而且需要更好地理解它们的横截面特性。也就是说，人们还想更多地了解跨多个时间序列的依赖结构。这是在金融投资组合分析中发现的一个问题，其中金融资产投资组合的价格动态和风险状况可能由数百个时间序列确定。该研究计划从结构和驱动噪声相关结构的角度看待多元广义扩散和多元Lévy过程。这种调查包括研究市场或经济中观察到的内在因素引起的一致性措施，这些因素可能影响价格过程的动态和风险管理中的核心对冲战略。在数学和统计学这些领域的进展可能会对市场效率的分析，定价和风险对冲，模型风险以及金融市场中更广泛的无套利概念产生直接影响。虽然这些领域对金融业特别感兴趣，但事实上，这些都是数据和信息数学中的重要问题。

Understanding the temporal random nature of data sequences is central to many areas of research, be it academic or industry-based. The financial industry, for example, is particularly interested in inferring information from large data sets and thus discovering any patterns revealed by recognising a signal. There is an additional dimension: not only is advancement in the statistical analysis and the Mathematics of random time series needed (temporal analysis), but also their cross-sectional properties need to be better understood. That is, one would also like to know more about the dependence structures across several time series. This is a problem found in financial portfolio analysis, among others, where the price dynamics and the risk profile of a portfolio of financial assets may be determined by hundreds of time series. This research programme treats multivariate generalised diffusions and multivariate Lévy processes from the perspective of structural and driving noise-based dependence structures. Such an investigation includes the study of concordance measures induced by endogenous factors, observed in the market or an economy, which may influence the dynamics of price processes and hedging strategies central in risk management. Progress in these areas of Mathematics and Statistics could have an immediate impact on the analysis of market efficiency, the pricing and hedging of risks, model risk, and the wider concept of no-arbitrage in financial markets. Although these areas are of particular interest to the financial industry, it is a fact that these are important questions in the Mathematics of Data and Information, in general.