In this paper, we consider inference in the context of a factor model for tensor-valued time series. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions. Building on the observation that such loss functions are adequate only if sufficiently many moments exist, we extend our results to the case of heavy-tailed distributions by considering estimators based on minimising the Huber loss function, which uses an $L_{1}$-norm weight on outliers. We show that such class of estimators is robust to the presence of heavy tails, even when only the second moment of the data exists.

翻译：本文考虑了张量值时间序列因子模型中的推断问题。我们研究了基于最小化二次损失函数的估计量在估计共同因子和载荷空间时的一致性。基于这样的观察：此类损失函数仅在足够多的矩存在时才适用，我们将结果推广到重尾分布的情况，通过考虑基于最小化Huber损失函数的估计量，该损失函数对异常值采用$L_{1}$范数权重。我们证明，即使数据仅存在二阶矩，此类估计量对重尾的存在也具有稳健性。