Functional Time Series Analysis
Greg Rice, University of Utah
Functional Data Analysis (FDA) is concerned with observations that are viewed as functions defined over some set. For example, the pollution level in a city on a given day can be thought of as a function defined on the time of day. Nearly all of the early asymptotic results from FDA are derived under the assumption that the observations are independent and identically distributed. A common source of functional data, however, is when long, continuous records are broken into segments of smaller, perhaps hourly or daily, curves. In this case, successive curves may exhibit dependencies, and Functional Time Series Analysis seeks to provide a flexible, nonparametric framework for studying such data. In this talk, we will first survey some of the central ideas of FDA, including principle component analysis, which is a commonly used technique in dimension reduction. We will then discuss the framework and theory of Functional Time Series Analysis. The talk will conclude with a more detailed application to the one-way functional analysis of variance problem and a study of electricity demand data from Adelaide, Australia.