Title: Dimension reduction for a stationary multivariate time series
Authors: Chung Eun Lee - University of Tennessee, Knoxville (United States) [presenting]
Xiaofeng Shao - University of Illinois at Urbana-Champaign (United States)
Abstract: A new methodology is introduced in order to perform dimension reduction for a stationary multivariate time series. Our method is motivated by the consideration of optimal prediction and focuses on the reduction of the effective dimension in conditional mean of time series given the past information. In particular, we seek a contemporaneous linear transformation such that the transformed time series has two parts with one part being conditionally mean independent of the past. To achieve this goal, we first propose the so-called martingale difference divergence matrix (MDDM), which can quantify the conditional mean independence of $V \in R^p$ given $U \in R^q$ and also encodes the number and form of linear combinations of $V$ that are conditional mean independent of $U$. Our dimension reduction procedure is based on eigen-decomposition of the cumulative martingale difference divergence matrix, which is an extension of MDDM to the time series context. Some theory is also provided about the rate of convergence of eigenvalue and eigenvector of the sample cumulative MDDM in the fixed-dimensional setting. Favorable finite sample performance is demonstrated via simulations and real data illustrations in comparison with some existing methods.