Asymptotic confidence intervals for impulse responses of near‐integrated processes

Abstract

Many economic time series are characterized by high persistence which typically requires nonstandard limit theory for inference. This paper proposes a new method for constructing confidence intervals for impulse response functions and half‐lives of nearly non‐stationary processes. It is based on inverting the acceptance region of the likelihood ratio statistic under a sequence of null hypotheses of possible values for the impulse response or the half‐life. This paper shows the consistency of the restricted estimator of the localizing constant which ensures the validity of the asymptotic inference. The proposed method is used to study the persistence of shocks to real exchange rates.