Functional Change-Point Asymptotics and Applications
Ansgar Steland
Institute of Statistics, RWTH Aachen University, Aachen, NRW, Germany

Present day statistical data collected in areas such as engineering, finance and econometrics or environmetrics is often characterized by three challenging features. Firstly, the data set is a time series, i.e. observations have a date stamp and are affected by temporal dependence. Secondly, the observations form a sequential data stream, i.e. when an observation is generated by the underlying data generating process, it is available to the statistician with no delay. Lastly, many data streams fit one the following two sampling designs dealing with functional data: i) Observations are taken at discrete time points and represent random functions of interest. ii) One observes a process in continuous time. In both cases, an important issue is to detect a change-points.

Focusing on procedures aiming at detecting change-points in functional data, we study control charts defined in terms of first exit stopping times of appropriately defined sequential empirical processes to which our theoretical results can be applied. We discuss recent limit theorems which generalize classical results to a large class of dependent time series which includes various known parametric classes such as ARMA models.

These results open the door to many fields of applications where time series matter. We carefully describe and discuss applications of the approach to challenging problems arising in applied statistics: Detecting departures from a reference signal to optimize multi-channel transmission in signal processing and communications engineering, measuring IV-curves of solar cells in photovoltaics, detecting structural economic changes in finance and econometrics as well as in environmetrics.

They also allowed us to propose and study a new solution based on empirical characteristic functions for the classic problem to simultaneously detect changes in the location and scale of a sequence of random variables.

Keywords: Change-point detection; Nonparametrics; Functional data analysis; Applications in finance, engineering and energy

Biography: Ansgar Steland studied mathematics, business administration and computer science at Göttingen University, where he also received his Ph.D., and Bonn University. He held assistant positions in applied statistics at Technische Universität Berlin and European University of Frankfurt/Oder. After being a lecturer at the Faculty of Mathematics of the Ruhr University of Bochum, he joined RWTH Aachen University where he holds the chair of stochastics at the Institute of Statistics. Focusing on nonparametric methodologies, his research interests cover many areas of probability and statistics including sequential change-point detection, (functional) nonparametric statistics, time series analysis, mathematical econometrics and financial statistics, statistics in photovoltaics and selected topics in engineering and computer science.