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Title: Gaussian approximation for high dimensional time series Authors:  Danna Zhang - University of California, San Diego (United States) [presenting]
Wei Biao Wu - University of Chicago (United States)
Abstract: High-dimensional time series data arise in a wide range of disciplines. The fact that the classical CLT for i.i.d. random vectors may fail in high dimensions makes high-dimensional inference notoriously difficult. More challenges are imposed by temporal and cross-sectional dependence. We will introduce the high-dimensional CLT for time series. Its validity depends on the sample size $n$, the dimension $p$, the moment condition and the dependence of the underlying processes. An example is taken to appreciate the optimality of the allowed dimension $p$. Equipped with the high-dimensional CLT result, we have a new sight on many problems such as inference for covariances of high-dimensional time series which can be applied in the analysis of network connectivity, inference for multiple posterior means in MCMC experiments, Kolmogorov-Smirnov test for high-dimensional time series data as well as inference for high-dimensional VAR models. We will also introduce an estimator for long-run covariance matrices and two resampling methods, i.e., Gaussian multiplier resampling and subsampling, to make the high-dimensional CLT more applicable. The results are then corroborated by a simulation study of an MCMC experiment based on a hierarchical model and real data analysis for high-dimensional time series.