Non-stationary functional time series and functional machine learning : inference and applications

• Main Author: Chen, Yichao
• Other Authors: PUN Chi Seng
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Science::Mathematics::Statistics
• Online Access: https://hdl.handle.net/10356/151903
• Institution: Nanyang Technological University

Functional time series analysis is important in the research of functional data, mainly in finance, also be involved in biology, medicine and many other areas. Stationary functional time series have many good properties that allow us to do the analysis and prediction with many existing methods. However, many of the functional time series data in our real world are nonstationary. Some of them may have a trend or just be random walks. For example, most of the stock price curves are nonstationary functional time series, which are difficult to perform analysis directly on these curves. In view of this, functional KPSS test and functional unit root test test can be important and have broad prospects of research and application. This thesis consists of two parts. In first part, we study the theory of statistical inference in nonstationary functional time series, including a bootstrap-based functional KPSS test and functional unit root test. If we test our functional data as i.i.d. or stationary data, we can consider to apply machine learning to analyze the functional data. In second part, we do an application on the functional data in chemistry. We apply different machine learning methods on the prediction of metallic nanoparticle size and size distribution from the functional data generated by the localized surface plasmon resonances (LSPRs). All of these predictions receive reliable results.