Martingale Difference Divergence Matrix and Its Application to Dimensional Reduction for Multivariate Time Series

• Activity Number: 489
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Chung Eun Lee* and Xiaofeng Shao
• Companies: and University of Illinois at Urbana-Champaign
• Keywords: Dimension reduction ; Multivariate volatility ; Factor model ; Conditional mean

Abstract

In this talk, we introduce a new methodology to reduce the dimension of multivariate time series. Our method is motivated from the consideration of optimal prediction and focuses on the reduction of the 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 finite sample performance is examined via simulations in comparison with some existing methods and also demonstrated in a data illustration.