We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as well as their remaining interconnectedness using a sparse VAR model. To handle heavy tails, we propose an element-wise data truncation step followed by a two-stage estimation procedure for estimating the latent factors and the VAR parameter matrices. Assuming the existence of the $(2 + 2ε)$-th moment only for some $ε\in (0, 1)$, we derive the rates of estimation which, making explicit the effect of heavy tails through $ε$, are comparable to the rates attainable in light-tailed settings as $ε\to 1$. Numerically, we demonstrate the competitive performance of the proposed estimators on simulated datasets and in an application to forecasting macroeconomics indicators.

翻译：我们研究了通过因子调整向量自回归（VAR）模型对高维重尾时间序列数据进行建模的问题。该模型同时通过少数因子解释变量的普遍协同变动，并利用稀疏VAR模型描述变量间的剩余关联性。为处理重尾性，我们提出逐元素数据截断步骤，随后采用两阶段估计程序估计潜在因子与VAR参数矩阵。在仅要求存在$(2+2ε)$阶矩（其中$ε\in(0,1)$）的假设下，我们推导了估计量收敛速率，该速率通过$ε$显式刻画了重尾性的影响，且当$ε\to 1$时与轻尾场景下可达到的速率相当。在数值实验中，我们通过模拟数据集和宏观经济指标预测应用验证了所提估计量的竞争性能。