Martingale Difference Divergence Matrix and Its Application to Dimension Reduction for Stationary Multivariate Time Series
鞅差散度矩阵及其在平稳多元时间序列降维中的应用
In this article, we introduce a new methodology 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…