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New Nonparametric Modeling Methods for High-Dimensional Time Series

高维时间序列的新非参数建模方法

基本信息

批准号：
1712558
负责人：
Shujie Ma
金额：
$ 12.5万
依托单位：
University of California-Riverside
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：
2017-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712558&HistoricalAwards=false
关键词：
New Nonparametric Modeling Methods Dimensional

项目摘要

Advances in modern technology have created numerous massive datasets, providing a great amount of information, but also new analysis challenges. The remarkable increase in the amount of data arises not only in the number of observations over time, but also in the number of variables that are simultaneously measured at each time. This results in high-dimensional time series data that are increasingly encountered in many fields, including finance, economics, genomics, social media, biomedical imaging, and so forth. High dimensional time series can be evolutionary, non-normally distributed, and/or heterogeneous. Methods for analyzing these types of data are still in their infancy due to the considerable methodological challenges encountered to describe their complex structure. Because of the intricacies of modern datasets, conventional statistical methods to extract information are often inappropriate. There is an immediate need for efficient and data-driven nonparametric methods to handle these problems. This project seeks to develop new nonparametric modelling methods with theoretical insights for structural change detection, robust estimation, heterogeneity exploration, and dynamic interdependency investigation. The project will help fill methodological gaps by greatly advancing the understanding of the intricacies of high-dimensional time series data. The new flexible methods may can benefit many scientific areas, including public health, medicine, economics, and the social sciences. The overall goal of this project is to develop new flexible statistical methods and theories to address the analytical challenges encountered in describing the evolutionary, non-normal, and heterogeneous features of high-dimensional time series data. This will be done via four inter-connected research topics. (1) A novel three-step method with theoretical guarantees will be developed for structural change detection and identification of factor models by exploiting nonparametric local estimation, shrinkage methods, and grid search techniques. The method can automatically detect breaks (if they exist) and identify their locations. (2) A new paradigm, covariate-assisted quantile latent factor models, is proposed for dimension reduction of high-dimensional time series. The method is robust to heavy-tailed distributions. The model assumptions are very general: the factors are unobserved, and both of the factors and their loadings can vary across quantiles. In addition, the method does not require moment conditions on the errors. (3) A concave fusion method is proposed for exploring heterogeneous functional curves driven by unobserved classes. The method permits structural change detection and heterogeneity exploration, which are difficult problems due to latent processes and the high-dimensional and dependence features in the data. (4) A new dimensionality reduction tool will be devised for a time-varying coefficient vector autoregressive model by exploiting non-centered functional principal component analysis. A novel computational estimation algorithm will be developed by combining proximal algorithms and optimization over Stiefel manifolds. The method can illuminate dynamic relationships in high dimensional nonstationary time series.

现代技术的进步创造了大量的海量数据集，提供了大量的信息，但也带来了新的分析挑战。数据量的显著增加不仅体现在随时间推移的观测数量上，而且体现在每次同时测量的变量数量上。这导致高维时间序列数据越来越多地出现在许多领域，包括金融，经济，基因组学，社交媒体，生物医学成像等。高维时间序列可以是演化的、非正态分布的和/或异构的。由于描述其复杂结构遇到了相当大的方法学挑战，分析这些类型数据的方法仍处于起步阶段。由于现代数据集的复杂性，传统的统计方法来提取信息往往是不合适的。有一个有效的和数据驱动的非参数方法来处理这些问题的迫切需要。该项目旨在开发新的非参数建模方法，为结构变化检测，稳健估计，异质性探索和动态相互依赖性调查提供理论见解。该项目将有助于填补方法上的空白，大大促进对高维时间序列数据的复杂性的理解。新的灵活方法可能会使许多科学领域受益，包括公共卫生，医学，经济学和社会科学。该项目的总体目标是开发新的灵活的统计方法和理论，以解决在描述高维时间序列数据的演化，非正态和异构特征时遇到的分析挑战。这将通过四个相互关联的研究课题来完成。(1)一种新的三步方法与理论保证将开发的结构变化检测和识别的因素模型，利用非参数局部估计，收缩方法，网格搜索技术。该方法可以自动检测断裂（如果存在）并识别其位置。(2)提出了一种新的高维时间序列降维模型-协变量辅助分位数潜在因子模型。该方法对重尾分布具有鲁棒性。模型假设非常一般：因子是不可观测的，并且因子及其载荷可以在分位数之间变化。此外，该方法不需要对误差的矩条件。(3)提出了一种凹融合方法，用于探索由不可观测类驱动的异质函数曲线。该方法允许结构变化检测和异构性探索，这是由于数据中的潜在过程和高维和依赖特征而造成的困难问题。(4)利用非中心函数主成分分析方法，设计了一种新的时变系数向量自回归模型降维工具。将近似算法与Stiefel流形上的优化相结合，提出了一种新的计算估计算法。该方法可以揭示高维非平稳时间序列的动态关系。