We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid inference procedures for the same parameters. Statistical inference in our setting is much more involved since standard procedures, like the delta-method, do not apply. By using local projection equations, we first construct a de-sparsified version of regularized estimators of the moving average parameters associated with the VAR system. We then obtain estimators of the structural impulse responses by combining the aforementioned de-sparsified estimators with a non-regularized estimator of the contemporaneous impact matrix, also taking into account the high-dimensionality of the system. We show that the distribution of the derived estimators of structural impulse responses has a Gaussian limit. We also present a valid bootstrap procedure to estimate this distribution. Applications of the inference procedure in the construction of confidence intervals for impulse responses as well as in tests for forecast error variance decomposition are presented. Our procedure is illustrated by means of simulations.

翻译：我们认为,在低层、结构高维矢量自动递减系统(SVAR)中,动力反应的统计推导值为零散、结构高维矢量自动递减系统(SVAR)中的动力反应的统计推算值。我们在高维环境中采用了一致的脉冲反应估计值,并提出了相同参数的有效推算程序。在我们的环境下,统计推论涉及更多,因为标准程序(如三角体方法)并不适用。我们首先使用本地投影方程式,构建了与VAR系统相关的移动平均参数的正常估计估计器的分解版。然后,我们通过将上述的分解估计值与同期影响矩阵的非常规估测算器相结合,并同时考虑到系统的高维度。我们通过模拟的方式展示了结构动力反应测算器的分布情况。我们还提出了一个用于估计这种分布的有效示意图的测测距程序。在构建脉冲反应的可信度间隔和预测误差位置测试中应用了推推法程序。我们用模拟的方法展示了我们的程序。