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High-dimensional vector autoregression with measurement error is frequentlyencountered in a large variety of scientific and business applications. In thisarticle, we study statistical inference of the transition matrix under thismodel. While there has been a large body of literature studying sparseestimation of the transition matrix, there is a paucity of inference solutions,especially in the high-dimensional scenario. We develop inferential proceduresfor both the global and simultaneous testing of the transition matrix. We firstdevelop a new sparse expectation-maximization algorithm to estimate the modelparameters, and carefully characterize their estimation precisions. We thenconstruct a Gaussian matrix, after proper bias and variance corrections, fromwhich we derive the test statistics. Finally, we develop the testing proceduresand establish their asymptotic guarantees. We study the finite-sampleperformance of our tests through intensive simulations, and illustrate with abrain connectivity analysis example.

Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error