Sufficient Dimension Reduction for Matrix and Tensor Time Series Data

• Activity Number: 542 - Recent Extension from Univariate to Multivariate Analysis for High-Dimensional Data with Complex Environment
• Type: Topic Contributed
• Date/Time: Thursday, August 6, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Seyed Yaser Samadi*
• Companies: Southern Illinois University, Carbondale
• Keywords: Dimension Reduction; Time Series

Abstract

Many data sets from across the sciences collect sequences of matrix- and array (tensor)-structured data; we refer to such data as tensor time series. Dimensionality reduction has always been one of the most fundamental and challenging tasks in high-dimensional data analysis. In the context of time series analysis, we mostly are interested in estimating and making inference about the conditional mean and variance functions of the time series variable at the current time given the previous lags. We develop dimension reduction procedures that incorporate dimensionality reduction schemes into the tensor-valued time series data that preserve sufficient information about the response. Particularly, we introduce the central mean and variance subspaces (CMVSs) for tensor-valued time series data. We study the properties of the CMVSs for the tensor time series and develop methods to estimate them. Simulation results and a real data analysis will be presented to demonstrate the effectiveness and use of the developed framework in analyzing tensor time series data.