A0198
Title: Tensor principal component analysis
Authors: Andrii Babii - University of North Carolina (United States) [presenting]
Eric Ghysels - University of North Carolina Chapel Hill (United States)
Abstract: New methods are developed 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. An estimation algorithm is proposed, 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. Theoretical results are provided on the consistency and asymptotic distribution for the tensor PCA estimator of loadings and factors. A novel test is also introduced for the number of factors based on the tail of the spectrum which is of independent interest. The tensor PCA and the test demonstrate good performance in Monte Carlo experiments and are applied to sorted portfolios.
