Estimation and inference for impulse response functions from univariate strongly persistent processes

This paper is concerned with the estimation and construction of confidence intervals for the impulse response function (IRF) from strongly persistent time series. A non-parametric, time domain estimator, based on an autoregressive (AR) approximation is shown to have good theoretical and small sample properties for the estimation of the IRF. An alternative procedure of using a semi-parametric local Whittle (LW) estimator of the long-memory parameter and then obtaining estimates of the short run parameters and IRF is also considered. The second part of the paper investigates the most appropriate methods for estimating the variability and the construction of confidence intervals for the estimated IRF. Particular attention is given to a generic semi-parametric sieve bootstrap based on an autoregressive approximation of the unknown data generating mechanism. The validity of bootstrap inference on the IRF, based on the autoregressive approximation, is proven under mild assumptions. The findings in this paper indicate that a good strategy for analysing IRF is to estimate by semi-parametric AR approximations, and to use the sieve bootstrap for estimating confidence intervals. Simulation evidence indicates this approach appears to be a very good strategy for processes with either short or long memory. An empirical example concerning the persistence of real exchange rate series is included.