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

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 $(2 + 2\epsilon)$-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.