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

TL;DR

This paper introduces a robust factor modeling approach for high-dimensional vector and tensor time series that effectively handles heavy-tailed data by combining tensor decomposition with data truncation, ensuring consistency and asymptotic normality.

Contribution

It develops a novel two-step tensor decomposition method with data truncation for heavy-tailed data, providing theoretical guarantees and practical criteria for factor number determination.

Findings

Method performs well in simulations with heavy tails.

Applications to macroeconomic data show improved robustness.

Theoretical results establish estimator consistency under minimal moment assumptions.

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 extreme observations with non-negligible probability. We propose to combine a two-step procedure for tensor 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 $(2 + 2\epsilon)$-th moment only for some $\epsilon \in (0, 1)$. Our rates explicitly depend on $\eps$ 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.