Impulse response analysis in infinite order cointegrated vector autoregressive processes

Various types of impulse responses have been used for interpreting finite order vector autoregressive (VAR) models in the stationary as well as the nonstationary cointegrated case. In practice, finite order VAR processes are regarded as rough approximations to the actual data generation process at best. Therefore we derive some general asymptotic results for infinite order cointegrated VAR processes that are used for inference on impulse responses. The theory is based on the assumption that finite order VARs are fitted to the time series of interest although the true order may be infinite. The order of the fitted process is, however, assumed to increase with the sample size. The theoretical results are illustrated by an empirical analysis of a German money demand system.