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Activity Number: 450
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 2:45 PM
Sponsor: Business and Economic Statistics Section
Abstract #321741
Title: A New Approach to Dimensional Reduction for Volatility of a Stationary Multivariate Time Series
Author(s): Chung Eun Lee* and Xiaofeng Shao
Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
Keywords: Volatility ; Nonlinear Dependence ; Principal Component ; Dimension Reduction

In this talk, we introduce a new methodology to reduce the dimension of a stationary multivariate time series focusing on the volatility matrix. Our method starts from martingale difference divergence matrix which considers the optimal prediction of a stationary multivariate time series. In particular, we seek a contemporaneous linear transformation such that the transformed time series has two parts with one part being conditionally variance independent of the past information. Our dimension reduction procedure is based on eigen-decomposition of the so-called cumulative volatility martingale difference divergence matrix, which encodes the number and form of linear combinations that are conditional variance independent of the past. We provide a simple way of estimating the number and the form of such type of linear combinations. The finite sample performance is examined via simulations in comparison with some existing methods and also demonstrated in a data illustration.

Authors who are presenting talks have a * after their name.

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