Statistical Analysis of Time Series Data

这个项目的重点是统计分析和开发算法，用于分析潜在的高维时间序列数据的各种来源，例如那些出现在经济学或物理学中的数据，以及合成数据的生成。众所周知，许多时间序列表现出违反诸如非平稳性等经典统计方法的假设的风格化特征，其中基础时间序列的统计特性随时间变化。该项目的一个目标是开发新的方法，以便能够根据这些关切进行有效的统计分析。高维数据从计算和统计的角度提出了新的挑战，在文献中被称为维度的诅咒。对包含许多变量的大型数据集进行有效分析可能在许多领域都是相关的，特别是在可能存在大量相关变量的经济情况下。对于后者，在许多应用程序和行业协作中，获取真实数据(通常是敏感的)是研究管道中的主要挑战和障碍。获得保留真实数据的结构属性的合成数据可以大大促进研究过程和与行业的互动。潜在应用的例子包括金融交易网络和限价订单账簿数据，在欺诈检测和金融市场监管等领域具有潜在影响。许多金融和经济时间序列具有潜在的隐藏因素，可能导致经济系统意外行为。这种隐藏因素可能是一小部分经济指标或实体，引领了许多其他指标或实体。因此，这些指标中的特殊冲击可能会对整个体系产生重大影响。该项目还旨在揭示这些隐藏的因素，因此将有助于评估由这些因素引起的系统性风险，这是英格兰银行等外部合作伙伴最感兴趣的话题。解决这个问题的方法超越了计量经济学文献中的传统方法，并来自无监督和有监督的机器学习工具和网络分析。该项目还将有助于进一步发展这两个领域，我们希望我们的发现对两个社区都有独立的兴趣。我们预计，我们的工作将引起英国政策制定者的兴趣，他们将能够更好地了解和量化英国实体或国内部门对外部全球因素的风险敞口。

This project focuses on statistical analysis and development of algorithms for analyzing various sources of potentially high-dimensional time-series data, such as those that appear in economics or physics, and also the generation of synthetic data. Many time series are known to exhibit stylised features that violate the assumptions of classical statistical methods such as non-stationarity, where the statistical properties of the underlying time-series change in time. A goal of the project is to develop new methodology to permit efficient statistical analysis in light of these concerns. High-dimensional data provides new challenges from both a computational and statistical perspective known in the literature as the curse of dimensionality. Efficient analysis of large data sets with many variables is likely to be relevant in many domains, particularly in economic situations where there may be a potentially very large number of relevant variables. In regards to the latter, in many applications and industry collaborations, getting access to real data (which is often sensitive) is a major challenge and barrier in the research pipeline. Having access to synthetic data that retains the structural properties of the real data could significantly facilitate the research process and interaction with industry. Examples of potential applications include financial transaction networks and limit order book data, with potential impact in areas such as fraud detection and financial market regulation.Many financial and economic time series have underlying hidden factors which may lead the economic system to behave unexpectedly. Such hidden factors could be a small set of economic indicators or entities which lead many of the other indicators or entities. Therefore, idiosyncratic shocks in these indicators could then have a significant effect on the whole system. This project is also aimed at revealing such hidden factors, and hence will aid assessing the systemic risk which arises from such factors, a topic of central interest to external partners such as Bank of England. The methods to tackle this problem go beyond traditional approaches from the econometrics literature, and are drawn from unsupervised and supervised machine learning tools, and network analysis. The project will also help to develop these two areas further, and we hope our findings to be of independent interest to both communities. We expect our work to be of interest for UK policy makers, who would be able to better understand and quantify the risk exposures of UK entities or domestic sectors to external global factors.