Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series

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 $(2 + 2\epsilon)$-th moment only for some $\epsilon \in (0, 1)$, we derive the rates of estimation which, making explicit the effect of heavy tails through $\epsilon$, are comparable to the rates attainable in light-tailed settings as $\epsilon \to 1$. Numerically, we demonstrate the competitive performance of the proposed estimators on simulated datasets and in an application to forecasting macroeconomics indicators.