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Abstract:
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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.
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