Dimension Reduction in Time Series via Central Subspaces

S. Yaser Samadi

Department of Mathematics

Southern Illinois University, Carbondale, IL 

Tuesday, Dec. 19, 2017, 11:00 -12:00

University of Tehran

School of Mathematics, Statistics and Computer Science

Hashtroodi hall

Abstract: Dimensionality reduction approaches have become an important problem in high dimensional data analysis. In the context of time series analysis, we are interested in estimating the conditional mean and the conditional variance functions. In this talk, we review some recently developed dimension reduction methods. Particularly, we introduce a notion of central mean and central variance subspaces (CMCVS) to capture the information contained in the conditional mean and the conditional variance functions of time series model. This is a sufficient dimension reduction method that can be utilized for nonlinear and non-stationary time series data. Nonparametric methods are used to estimate the CMCVS. The proposed estimators are shown to be consistent. Some numerical studies are presented to corroborate the theoretical results.