Estimation and Inference for Impulse Response Weights From Strongly Persistent Processes

This paper considers the problem of estimating impulse response weights (IRW s) from processes that may be strongly dependent and the related issue of constructing confidence intervals for the estimated IRW s. We compare several approaches including QMLE, and a two step estimator that uses a semi parametric estimate of the long memory parameter in the first step, and also an estimator from fitting an autoregressive approximation. A main focus of the paper concerns the most appropriate method for constructing confidence intervals for the IRW s. We show that the parametric bootstrap is valid under very weak conditions, including non Gaussianity, for making inference on IRW from possibly strongly dependent processes. We also propose, and justify theoretically, a semi-parametric sieve bootstrap based on autoregressive approximations that can be used for IRW s obtained by autoregressive approximations. We find that estimates of IRW based on autoregressive approximations and also confidence intervals of IRW s based on the sieve bootstrap generally have very desirable properties and are shown to perform well in a detailed simulation study. Finally, we apply the methods we develop to an extensive and detailed empirical application on inflation and real exchange rate data.