Tensor Principal Component Analysis

39 Pages Posted: 4 Jan 2023 Last revised: 14 Apr 2023

See all articles by Andrii Babii

Andrii Babii

University of North Carolina at Chapel Hill

Eric Ghysels

University of North Carolina Kenan-Flagler Business School; University of North Carolina (UNC) at Chapel Hill - Department of Economics

Junsu Pan

University of North Carolina at Chapel Hill

Date Written: December 25, 2022

Abstract

In this paper, we develop new methods for analyzing high-dimensional tensor datasets. A tensor factor model describes a high-dimensional dataset as a sum of a low-rank component and an idiosyncratic noise, generalizing traditional factor models for panel data. We propose an estimation algorithm, called tensor principal component analysis (PCA), which generalizes the traditional PCA applicable to panel data. The algorithm involves unfolding the tensor into a sequence of matrices along different dimensions and applying PCA to the unfolded matrices. We provide theoretical results on the consistency and asymptotic distribution for tensor PCA estimator of loadings and factors. The algorithm demonstrates good performance in Mote Carlo experiments and is applied to sorted portfolios.

Keywords: Principal component analysis, tensor data, singular value and canonical polyadic decompositions

JEL Classification: C10, C33, C38, C55

Suggested Citation

Babii, Andrii and Ghysels, Eric and Pan, Junsu, Tensor Principal Component Analysis (December 25, 2022). Available at SSRN: https://ssrn.com/abstract=4312303 or http://dx.doi.org/10.2139/ssrn.4312303

Andrii Babii (Contact Author)

University of North Carolina at Chapel Hill ( email )

Gardner Hall, CB 3305
Chapel Hill, NC 27514
United States

Eric Ghysels

University of North Carolina Kenan-Flagler Business School ( email )

Kenan-Flagler Business School
Chapel Hill, NC 27599-3490
United States

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Gardner Hall, CB 3305
Chapel Hill, NC 27599
United States
919-966-5325 (Phone)
919-966-4986 (Fax)

HOME PAGE: http://https://eghysels.web.unc.edu/

Junsu Pan

University of North Carolina at Chapel Hill ( email )

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