  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.
