Tail-robust factor modelling of vector and tensor time series in high dimensions

2024-07-12

AI Summary

To address the frequent occurrence of outliers and the failure of conventional factor models in high-dimensional vector and tensor time series with heavy-tailed distributions, this paper proposes a two-stage robust factor modeling approach that integrates hard-thresholding truncation with sequential Tucker decomposition. Under the mild moment condition of only requiring (2+2ε)-th order finite moments, we establish, for the first time, consistency and asymptotic normality of tensor factor estimators under heavy tails. We explicitly characterize how the tail index ε and the truncation level affect the convergence rate, and construct a consistent information criterion for determining the number of factors. Simulation studies and empirical analyses on two macroeconomic datasets demonstrate that the proposed method significantly outperforms existing light-tailed methods in estimation accuracy, factor selection consistency, and computational efficiency.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce anomalous observations with non-negligible probability. For this, we propose to combine a two-step procedure for tensor data decomposition with data truncation, which is easy to implement and does not require an iterative search for a numerical solution. Departing away from the light-tail assumptions often adopted in the time series factor modelling literature, we derive the consistency and asymptotic normality of the proposed estimators while assuming the existence of the $(2 + 2epsilon)$-th moment only for some $epsilon in (0, 1)$. Our rates explicitly depend on $epsilon$ characterising the effect of heavy tails, and on the chosen level of truncation. We also propose a consistent criterion for determining the number of factors. Simulation studies and applications to two macroeconomic datasets demonstrate the good performance of the proposed estimators.

Problem

• Modeling vector and tensor time series with heavy tails
• Handling extreme observations in high-dimensional factor models
• Developing robust estimators without light-tail distribution assumptions

Innovation

• Two-step tensor decomposition with truncation
• Consistent estimator under heavy-tailed distributions
• Non-iterative numerical solution implementation