Estimation and Inference in Functional Time Series Analysis

本文旨在拓展泛函时间序列分析(FTSA)的理论和应用。函数数据分析在20世纪90年代的S时期开始出现，早期的发展集中在简单的随机样本观察，可以框架为曲线或函数。然而，功能数据通常是通过将几乎连续的时间记录分成更小的段来顺序获得的。例如，可以对污染水平的高频记录进行分段，以形成一系列每日污染曲线。其他例子包括顺序观察的描述物理现象的功能，如在功能磁共振成像中，描述大脑中血流的功能是随着时间的推移而计算出来的。在这些情况下，简单随机样本的假设往往太过强烈，于是一个中心问题变成了如何在这样复杂的数据中解释和利用时间相关性。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在两个主要方向上扩展了FTSA的知识：

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: