CDS&E: Statistical Methodology for Analysis and Forecasting with Large Scale Temporal Data

技术进步使得能够收集随着时间的推移而演变的大型复杂数据。这些数据还表现出跨多个实体（例如国家、患者）的异质性，并且在许多情况下以不同的频率进行采样和收集。因此，迫切需要开发和定制数据分析技术，以满足多个变量之间存在时间依赖性所提出的具体要求，并解决不同的采样频率和异质性问题。 该项目开发的统计学习模型和相关分析方法将适用于广泛的领域，包括宏观经济和金融数据的分析和预测以及神经科学。基于该项目工作的实证工作将提供有关大脑区域功能连接的见解，但也量化了患有常见疾病的受试者的异质性程度。它们还将有助于政策制定者和金融监管机构制定监测计划，评估整个市场的压力状况。此外，我们预计将有大量的技术转移到其他应用领域，如环境科学，在这些领域可以获得以异质性和混合频率采样为特征的类似类型的数据。为了应对数据的时间依赖性、异质性和不同采样频率的挑战，该项目将：（i）基于新的先验分布，开发和研究高维时间序列数据的向量自回归（VAR）模型的贝叶斯版本，（ii）在VAR模型中引入结构稀疏性，并引入外生变量，（iii）发展可容纳强相关特质成分的近似动态因子模型，（iv）发展相关VAR模型的联合估计方法，最后（v）发展处理混合频率时间序列数据的贝叶斯方法。一个强烈的重点放在提供不确定性量化的模型参数，这是特别重要的应用程序中，通常缺乏许多现代方法的大型数据集。该项目将推进大数据设置的最新技术，涉及建模，计算和推理前沿的大量时间序列。最后，博士生将在时间序列建模、分析和预测方面获得新颖、及时的主题指导，课程设置将得到提升。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

Technological advances have enabled the collection of large, complex data that evolve over time. Such data also exhibit heterogeneity across multiple entities (e.g. countries, patients) and on many occasions are sampled collected) at different frequencies. Hence, there is a strong need for developing and tailoring data analysis techniques to the specific requirements imposed by the presence of temporal dependence across multiple variables and also address varying sampling frequency and heterogeneity issues. The statistical learning models, and associated analysis methods developed in this project would be applicable across a wide range of fields, including analysis and forecasting with macroeconomic and financial data and in neuroscience. Empirical work based on the work of this project would provide insights on functional connectivity of brain regions, but also quantify the degree of heterogeneity of subjects suffering from a common disease. They would also be useful to policy makers and financial regulators for devising monitoring schemes that assess stress conditions across markets. Further, we expect significant technology transfer to other application areas, such as environmental sciences where similar types of data, characterized by heterogeneity and mixed frequency sampling, are available. To address the challenges of temporal dependence, heterogeneity and varying sampling frequency in the data this project would: (i) develop and investigate Bayesian versions of Vector Autoregressive (VAR) models for high-dimensional time series data, based on novel prior distributions, (ii) introduce structured sparsity in VAR models and also incorporate exogenous variables, (iii) develop approximate dynamic factor models that can accommodate strongly correlated idiosyncratic components, (iv) develop methods for joint estimation of related VAR models and finally (v) develop Bayesian methodology for handling mixed frequency time series data. A strong emphasis is placed on providing uncertainty quantification of the model parameters, which is particularly important in applications and is usually lacking in many modern methods for large data sets. This project would advance the state of the art for Big Data settings involving a large number of time series both at the modeling, computational and inference fronts. Finally, doctoral students would receive mentoring in novel, timely topics on time series modeling, analysis and forecasting and course curriculum would be advanced.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.