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

随着时间的推移，技术的进步使得大量复杂数据的收集成为可能。这些数据在多个实体（如国家、患者）之间也表现出不同频率的异质性，在许多情况下是抽样收集的。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的时间依赖性所施加的特定要求，并解决不同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。基于该项目的实证工作将提供对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。它们还有助于政策制定者和金融监管机构制定监测方案，评估整个市场的压力状况。此外，我们期望重大的技术转移到其他应用领域，例如环境科学，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。为了解决数据的时间依赖性、异质性和不同采样频率的挑战，本项目将：(i)开发和研究基于新颖先验分布的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模型中引入结构化稀疏性，并纳入外生变量，（iii）开发可以容纳强相关特质成分的近似动态因子模型，（iv）开发相关VAR模型的联合估计方法，最后(v)开发处理混合频率时间序列数据的贝叶斯方法。重点放在提供模型参数的不确定性量化，这在应用中特别重要，并且通常在许多大型数据集的现代方法中缺乏。该项目将在建模、计算和推理方面推进涉及大量时间序列的大数据设置的最新技术。最后，在时间序列建模、分析和预测等新颖、及时的课题上对博士生进行指导，并推进课程设置。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.