Tail-robust factor modelling of vector and tensor time series in high dimensions
针对数据存在重尾（产生极端观测）的向量和张量时间序列，提出结合数据截断的两步张量分解方法，在仅需存在2+2ε阶矩的弱假设下证明估计量的一致性和渐近正态性，并给出因子数的一致选择准则。
Summary 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 nonnegligible probability. We propose combining 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 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 $, characterizing the effect of heavy tails and 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 strong performance of the proposed estimators.