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 with data truncation, which is easy to implement and does not require iteratively searching for a numerical solution. Departing away from the light-tail assumptions often adopted in the time series factor modelling literature, we derive the theoretical properties of the proposed estimators while only assuming the existence of the $(2 + 2\eps)$-th moment for some $\eps \in (0, 1)$, fully characterising the effect of heavy tails on the rates of estimation as well as the level of truncation. Numerical experiments on simulated datasets demonstrate the good performance of the proposed estimator, which is further supported by applications to two macroeconomic datasets.

翻译：我们研究在数据存在重尾分布的情况下，对向量和张量值时间序列进行因子建模的问题，这种重尾分布会以不可忽略的概率产生异常观测值。为此，我们提出将两步法与数据截断相结合，该方法易于实现，且无需迭代搜索数值解。与时间序列因子建模文献中常采用的轻尾假设不同，我们在仅假设存在某个 $\eps \in (0, 1)$ 的 $(2 + 2\eps)$ 阶矩的条件下，推导了所提出估计量的理论性质，完整刻画了重尾对估计速率以及截断水平的影响。在模拟数据集上的数值实验证明了所提出估计量的良好性能，这进一步得到了在两个宏观经济数据集上应用结果的支持。