Asymptotic Confidence Intervals for Impulse Responses of Near-Integrated Processes: An Application to Purchasing Power Parity

Many economic time series are charecterized by high persistence which typically requires nonstandard limit theory for inference. This paper proposes a new method for constructing confidence intervals for the impulse response functions of nearly nonstationary processes. The method is based on inverting the acceptance region of the LR statistic evaluated under a sequence of null hypotheses of possible values for the impulse response. Under the null, the LR statistic can be represented as a ratio of functionals of Ornstein-Uhlenbeck processes and its asymptotic quantiles can be simulated easily. The method is extended to multivariate processes with near-unit roots. The empirical results for the real exchange rates show some support for 3-5 year half-lives reported by Rogoff (1996).