A truncation-based two-stage estimator for factor-adjusted VAR models achieves estimation rates comparable to light-tailed cases under only (2+2ε) moments for ε in (0,1).
Proof.By recursively using Minkowski’s inequality we have that for all 1≤i≤p: ∥Xit∥2+2ϵ ≤λ i1∥F1t∥2+2ϵ +· · ·+λ ir∥Frt∥2+2ϵ +∥ξ it∥2+2ϵ
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Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series
A truncation-based two-stage estimator for factor-adjusted VAR models achieves estimation rates comparable to light-tailed cases under only (2+2ε) moments for ε in (0,1).