Date of Award

2010

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Piotr Kokoszka

Abstract

Functional data analysis (FDA) is a relatively new branch of statistics that has seen a lot of expansion recently. With the advent of computer processing power and more efficient software packages we have entered the beginning stages of applying FDA methodology and techniques to data. Part of this undertaking should include an empirical assessment of the effectiveness of some of the tools of FDA, which are sound on theoretical grounds. In a small way, this project helps advance this objective.

This work begins by introducing FDA, scalar prediction techniques, and the functional autoregressive model of order one - FAR(1). Two functional data prediction methods are discussed in detail. One method uses the estimator Ψp (Bosq, 2000), while the other finds the predictive loadings, which are the paths in a Hilbert space most relevant for prediction (Kargin and Onatski, 2008). A functional data simulation is carried out and used to compare the efficacy of the two methods. The design and results (presented in both graphs and numerical tables) are explained in-depth. Finally, conclusions are drawn and future work is outlined.

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