Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Time Series

• Activity Number: 132 - Functional Data and Time Series
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Seyed Yaser Samadi* and Priyan Alwis
• Companies: Southern Illinois University, Carbondale and Southern Illinois University, Carbondale
• Keywords: Time Series ; Fourier transform; Central Subspace ; Central mean subspace; Dimension reduction ;

Abstract

Dimensionality reduction has always been one of the most important and challenging problems in high-dimensional data analysis. In the context of time series analysis, we are interested in estimating the conditional mean and variance functions. Using the central and central mean subspaces, that preserve sufficient information about the response, one can estimate the unknown mean and variance functions. There are different approaches in the literature to estimate the time series central and central mean subspaces. However, those methods are computationally intensive and not feasible in practice. Using the Fourier transform, we estimate the time series central subspace and central mean subspace. The proposed estimators are shown to be consistent. Simulation results are presented to support the theoretical findings.