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Simultaneous inference for high-dimensional non-Gaussian time series isalways considered to be a challenging problem. Such tasks require not onlyrobust estimation of the coefficients in the random process, but also derivinglimiting distribution for a sum of dependent variables. In this paper, wepropose a multiplier bootstrap procedure to conduct simultaneous inference forthe transition coefficients in high-dimensional non-Gaussian vectorautoregressive (VAR) models. This bootstrap-assisted procedure allows thedimension of the time series to grow exponentially fast in the number ofobservations. As a test statistic, a de-biased estimator is constructed forsimultaneous inference. Unlike the traditional de-biased/de-sparsifying Lassoestimator, robust convex loss function and normalizing weight function areexploited to avoid any unfavorable behavior at the tail of the distribution. Wedevelop Gaussian approximation theory for VAR model to derive the asymptoticdistribution of the de-biased estimator and propose a multiplierbootstrap-assisted procedure to obtain critical values under very mild momentconditions on the innovations. As an important tool in the convergence analysisof various estimators, we establish a Bernstein-type probabilisticconcentration inequality for bounded VAR models. Numerical experiments verifythe validity and efficiency of the proposed method.

High-dimensional Simultaneous Inference on Non-Gaussian VAR Model via De-biased Estimator