CP Factor Model for Dynamic Tensors

TL;DR

This paper introduces a novel CP tensor factor model for analyzing high-dimensional dynamic tensor time series, emphasizing unique loading vectors and a new projection estimator, with theoretical and empirical validation.

Contribution

It proposes a CP-based tensor factor model with a new estimator, differing from Tucker models, and provides theoretical error bounds and practical applications.

Findings

The model effectively captures dynamic tensor data.

The new estimator has favorable statistical properties.

Applications demonstrate interpretability and accuracy.

Abstract

Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.