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 accommodate heavy tails, we adopt an element-wise 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 that make explicit the effect of heavy tails through $\epsilon$. Simulation studies and an application in macroeconomics demonstrate the competitive performance of the proposed estimators.