Impulse Response Analysis for Sparse High-Dimensional Time Series

We consider structural impulse response analysis for sparse high-dimensional vector autoregressive (VAR) systems. Since standard procedures like the delta-method do not lead to valid inference in the high-dimensional set-up, we propose an alternative approach. First, we directly construct a de-sparsified version of the regularized estimators of the moving average parameters that are associated with the VAR process. Second, the obtained estimators are combined with a de-sparsified estimator of the contemporaneous impact matrix in order to estimate the structural impulse response coefficients of interest. We show that the resulting estimator of the impulse response coefficients has a Gaussian limiting distribution. Valid inference is then implemented using an appropriate bootstrap approach. Our inference procedure is illustrated by means of simulations and real data applications.