Estimation and Inference in Functional Time Series Analysis

函数时间序列分析中的估计和推理

• 批准号: RGPIN-2016-03723
• 负责人: Rice, Gregory
• 金额: $ 1.97万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635792
• 关键词: Estimation; Inference; Functional; Time; Series

This proposal aims to extend the theory and applications of functional time series analysis (FTSA). Functional data analysis (FDA) came into prominence in the 1990's, and the early developments focused on simple random samples of observations that can be framed as curves or functions. Functional data are, however, often obtained sequentially by breaking nearly continuous time records into smaller segments. For example, high frequency records of pollution levels may be segmented to form a series of daily pollution curves. Other examples include sequentially observed functions that describe physical phenomena, as in functional magnetic resonance imaging, where functions describing blood flow in the brain are computed over time. The assumption of a simple random sample is often too strong in these cases, and a central issue then becomes how to account for and utilize temporal dependence in such complex data. FTSA provides theory and methodology for addressing this issue. The research outlined in this proposal expands the knowledge of FTSA in two primary directions:

本文旨在扩展功能时间序列分析（FTSA）的理论与应用。功能数据分析（FDA）在20世纪90年代开始崭露头角，早期的发展集中在简单的随机观察样本上，这些样本可以被框定为曲线或函数。然而，功能数据通常是通过将几乎连续的时间记录分解成更小的片段来顺序获得的。例如，污染水平的高频记录可以分割成一系列的日污染曲线。其他例子包括描述物理现象的顺序观察功能，如在功能磁共振成像中，描述大脑血液流动的功能随着时间的推移而计算。在这些情况下，简单随机样本的假设往往过于强烈，然后一个中心问题就变成了如何在如此复杂的数据中解释和利用时间依赖性。FTSA为解决这一问题提供了理论和方法。本提案中概述的研究从两个主要方向扩展了FTSA的知识：