Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models

This paper provides closed-form formulae for computing the asymptotic standard errors of the estimated autocovariance and autocorrelation functions for stable VAR models by means of the d-method. These standard errors can be used to construct asymptotic confidence bands for the estimated autocovariance and autocorrelation functions in order to assess the underlying estimation uncertainty. A Monte Carlo experiment gives evidence on the small-sample performance of these asymptotic confidence bands compared with that obtained using bootstrap methods. The usefulness of the asymptotic confidence bands for empirical work is illustrated by two applications to euro area data on inflation, output and interest rates.