A0987
Title: Sufficient dimension reduction for high dimensional nonlinear vector autoregressive models
Authors: Jiaying Weng - Bentley University (United States) [presenting]
Abstract: The vector autoregressive model is a fundamental tool for modeling multivariate time series data. It is widely used in various fields, such as economics, finance, and climate studies. One of the challenges in modeling high-dimensional time series data is the curse of dimensionality, particularly when incorporating multiple time series and increasing the order of the vector autoregressive model. The purpose is to explore sufficient dimension reduction in nonlinear vector autoregressive models, where the present vector is influenced by multiple indices defined on past lags. The proposed sufficient dimension reduction approaches aim to identify these indices from the past information of the multivariate time series. Specifically, several linear combinations of the covariate vector are sought, comprising past lags, such that the current response vector is conditionally independent of the covariate vector given the linear combination. The linear combinations depict the time series' central subspace, the ultimate goal of sufficient dimension reduction. A time series martingale difference divergence matrix method is proposed for the nonlinear vector autoregressive models to estimate the central subspace. For high-dimensional time series, a sparse estimation procedure is developed to identify the central subspace using a penalized optimization problem.
