Dissertation/Thesis Abstract

Invariance principles in functional time series analysis with applications
by Rice, Gregory, Ph.D., The University of Utah, 2015, 110; 3746458
Abstract (Summary)

This dissertation aims to develop the theory and applications of functional time series analysis. Functional data analysis came into prominence in the 1990s when more sophisticated data collection and storage systems became prevalent, and many of the early developments focused on simple random samples of curves. However, a common source of functional data is when long, continuous records are broken into segments of smaller curves. An example of this is geologic and economic data that are presented as hourly or daily curves. In these instances, successive curves may exhibit dependencies which invalidate statistical procedures that assume a simple random sample.

The theory of functional time series analysis has grown tremendously in the last decade to provide methodology for such data, and researchers have focused primarily on adapting methods available in finite dimensional time series analysis to the function space setting. As a first problem, we consider an invariance principle for the partial sum process of stationary random functions. This theory is then applied to the problems of testing for stationarity of a functional time series and the one-way functional analysis of variance problem under dependence.

Indexing (document details)
Advisor: Horvath, Lajos
Commitee: Alberts, Tom, Ethier, Stewart, Khoshnevisan, Davar, Kiefer, David
School: The University of Utah
Department: Mathematics
School Location: United States -- Utah
Source: DAI-B 77/05(E), Dissertation Abstracts International
Subjects: Mathematics, Statistics
Keywords: Analysis of variance, Functional data, Time series, Weak convergence
Publication Number: 3746458
ISBN: 978-1-339-39867-9
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