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

技术进步使收集随时间演变的大型、复杂数据成为可能。这些数据还显示出在多个实体(例如国家、患者)之间的异质性，并在许多情况下以不同的频率采集样本。因此，迫切需要开发和调整数据分析技术，以满足因多个变量之间存在时间相关性而产生的具体要求，并解决不同的采样频率和异质性问题。本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，包括利用宏观经济和金融数据以及神经科学进行分析和预测。基于该项目工作的经验性工作将提供对大脑区域功能连接的洞察，也将量化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设计监测方案，评估各市场的压力状况。此外，我们预计将有大量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抽样为特征的类似类型的数据。为了解决数据中的时间相关性、异质性和采样频率变化的挑战，本项目将：(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考虑外部变量；(Iii)开发能够适应强相关特性分量的近似动态因素模型；(Iv)开发相关VAR模型的联合估计方法；以及(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上，这在应用中特别重要，在许多用于大数据集的现代方法中通常缺乏这一点。该项目将推动在建模、计算和推理方面涉及大量时间序列的大数据设置的最新水平。最后，博士生将接受关于时间序列建模、分析和预测的新颖、及时的主题的指导，课程课程将得到提升。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.