Statistical Models, Inference, and Computation for Multidimensional Time Series Data

多维时间序列数据的统计模型、推理和计算

• 批准号: 1712966
• 负责人: Vladas Pipiras
• 金额: $ 20万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712966&HistoricalAwards=false
• 关键词: Statistical; Models; Inference; Computation; Multidimensional

It is now commonplace for data to be collected over time across multiple (often many) sources. Examples include the time signals across multiple brain regions arising from fMRI, ocean wave height series across multiple spatial locations collected from buoys or satellites, and the multiple economic indicators (GPD, unemployment, and so on) gathered over time by government agencies and other parties. Available techniques often either neglect temporal dependencies for such high-dimensional data arising from multiple sources or do not apply to situations when the number of sources is large. This research project aims to develop novel statistical modeling tools that can capture adequately both the temporal features of such data and also their dependencies across multiple sources. Such tools have the potential to greatly enhance knowledge gained from such data. With fMRI data, for example, proper accounting for temporal dependence and large number of brain regions may facilitate better distinction among various clinical categories (ADHD, autism, etc.). Understanding the temporal and spatial dependencies in wave height data can lead to better predictions of storm activity across the oceans, and further insight into economic activity is expected from improved analysis of multiple economic indicators.The project aims at developing an integrated approach to analyzing large multidimensional time series data, including their statistical models, estimation, computation (algorithms), and practice. The research covers both short-range and long-range dependent multidimensional time series. For short-range dependent series, the focus is on sparse vector autoregressive and related models, dimension reduction, change point detection and some nonlinear models. The problems to be addressed concern regularization techniques, statistical significance, models exhibiting cyclical variations and other issues. Multidimensional long-range dependence is suggested as the important class complementing vector autoregressive and related short-range dependent series, thus gathering the two general classes of models employed in modern time series analysis. The goal is to develop a new methodology for multidimensional long-range dependent series with the so-called general phase, which controls the symmetry properties of multidimensional time series, in both linear and nonlinear settings. The developed methods should be useful across a wide range of areas, including neuroscience, oceanography and environmental sciences, geophysics, economics and finance, and others.

现在，随着时间的推移跨多个（通常是多个）来源收集数据已经很常见。 例子包括功能磁共振成像产生的跨多个大脑区域的时间信号、从浮标或卫星收集的跨多个空间位置的海浪高度序列，以及政府机构和其他各方随着时间的推移收集的多种经济指标（GPD、失业率等）。现有技术通常要么忽略来自多个源的此类高维数据的时间依赖性，要么不适用于源数量很大的情况。该研究项目旨在开发新颖的统计建模工具，能够充分捕获此类数据的时间特征及其跨多个来源的依赖性。此类工具有可能极大地增强从此类数据中获得的知识。例如，利用功能磁共振成像数据，正确考虑时间依赖性和大量大脑区域可能有助于更好地区分各种临床类别（多动症、自闭症等）。了解波高数据的时间和空间依赖性可以更好地预测跨洋风暴活动，并通过改进对多个经济指标的分析来进一步了解经济活动。该项目旨在开发一种综合方法来分析大型多维时间序列数据，包括其统计模型、估计、计算（算法）和实践。该研究涵盖短期和长期相关的多维时间序列。对于短程相关序列，重点是稀疏向量自回归和相关模型、降维、变化点检测和一些非线性模型。要解决的问题涉及正则化技术、统计显着性、表现出周期性变化的模型和其他问题。多维长程相关被认为是补充向量自回归和相关短程相关序列的重要类别，从而聚集了现代时间序列分析中使用的两类通用模型。目标是开发一种具有所谓一般相位的多维长程相关序列的新方法，该方法在线性和非线性设置下控制多维时间序列的对称性。所开发的方法应该适用于广泛的领域，包括神经科学、海洋学和环境科学、地球物理学、经济学和金融学等。

项目成果

Periodic dynamic factor models: estimation approaches and applications

周期性动态因子模型：估计方法和应用

• DOI: 10.1214/18-ejs1518
• 发表时间: 2018
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Baek, Changryong;Davis, Richard A.;Pipiras, Vladas
• 通讯作者: Pipiras, Vladas

Asymptotics of bivariate local Whittle estimators with applications to fractal connectivity

双变量局部 Whittle 估计量的渐近及其在分形连通性中的应用

• DOI: 10.1016/j.jspi.2019.07.007
• 发表时间: 2020
• 期刊: Journal of Statistical Planning and Inference
• 影响因子: 0.9
• 作者: Baek, Changryong;Kechagias, Stefanos;Pipiras, Vladas
• 通讯作者: Pipiras, Vladas

Semiparametric, parametric, and possibly sparse models for multivariate long-range dependence

用于多元远程依赖性的半参数、参数和可能的稀疏模型

• DOI: 10.1117/12.2275101
• 发表时间: 2017
• 期刊: Wavelets and Sparsity XVII
• 作者: Pipiras, Vladas;Kechagias, Stefanos;Baek, Changryong
• 通讯作者: Baek, Changryong

Two sample tests for high-dimensional autocovariances

• DOI: 10.1016/j.csda.2020.107067
• 发表时间: 2021-01
• 期刊: Comput. Stat. Data Anal.
• 作者: Changryong Baek;K. Gates;Benjamin Leinwand;V. Pipiras

Stationary subspace analysis of nonstationary covariance processes: Eigenstructure description and testing

非平稳协方差过程的平稳子空间分析：特征结构描述和测试

• DOI: 10.3150/20-bej1243
• 发表时间: 2021
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Sundararajan, Raanju R.;Pipiras, Vladas;Pourahmadi, Mohsen
• 通讯作者: Pourahmadi, Mohsen