Abstract: In this talk, we introduce a new methodology to reduce the number of parameters in multivariate time series modeling. Our method is motivated from 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 information. Our dimension reduction procedure is based on eigen-decomposition of the so-called cumulative martingale difference divergence matrix, which encodes the number and form of linear combinations that are conditional mean independent of the past. Interestingly, there is a factor model representation for our dimension reduction framework and our method can be further extended to reduce the dimension of volatility matrix. We provide a simple way of estimating the number of factors and factor loading space, and obtain some theoretical results about the estimators. The new method is applied to GDP and 7-city temperature series to illustrate the usefulness of the new approach.