Multiple Change Point Analysis Of Multivariate Data Via Energy Statistics
In this dissertation we consider the offline multiple change point problem. More specifically we are interested in estimating both the number of change points, and their locations within a given multivariate time series. Many current works in this area assume that the time series observations follow a known parametric model, or that there is at most one change point. This work examines the change point problem in a more general setting, where both the observation distributions and number of change points are unknown. Our goal is to develop methods for identifying change points, while making as few unrestrictive assumptions as possible. The following chapters are a collections of works that introduced new nonparametric change point algorithms. These new algorithms are based upon E-Statistics and have the ability to detect any type of distributional change. The theoretical properties of these new algorithms are studied, and conditions under which consistent estimates for the number of change point and change point locations are presented. These newly proposed algorithms are used to analyze various dataset, ranging from financial time series to emergency medical service data. Efficient implementations of these algorithms are provided by the R package ecp. A portion of this dissertation is devoted to the discussion of the implementation of these algorithms, as well as the use of the software package.
Renegar,James; Jarrow,Robert A.
Ph.D. of Operations Research
Doctor of Philosophy
dissertation or thesis