B0626
Title: On lagged covariance and cross-covariance operators of processes in cartesian products of abstract Hilbert Spaces
Authors: Sebastian Kuehnert - University of Bochum (Germany) [presenting]
Abstract: A key concern in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool. Probabilistic features of and estimators for lagged covariance operators of stationary processes with values in $L^2[0,1]$, the space of measurable, square-Lebesgue integrable real-valued functions with domain [0,1], are widely studied for fixed lag, and under several limitations also in further spaces. Lagged cross-covariance operators of stationary processes in $L^2[0,1]$ were also comprehensively studied. Core results on lagged covariance and cross-covariance operators of processes in cartesian products of abstract Hilbert spaces are reviewed. Motivating examples for the use of processes in such Cartesian products are given. Estimators and asymptotic upper bounds of the estimation errors for the lagged covariance and cross-covariance operators of processes in these Cartesian products are deduced for fixed as well as increasing lag and Cartesian powers. The processes are allowed to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, estimators for the principle components of our covariance operators are discussed, and a simulation study is performed on well-established time series.
