Impulse response and forecast error variance asymptotics in nonstationary VARs
This paper studies the role of prior information on asymptotic forecast performance and policy analysis based on vector autoregressive models (VARs). These models have several alternative representations -- error correction models (ECMs), reduced rank regression (RRR) models -- which provide different ways to encode prior information about non-stationarity. The role of prior information on properties of estimators of VARs, ECMs and RRR models is well understood. In general it improves efficiency and may provide unbiasedness. However, for forecasting and policy analysis purposes impulse responses and forecast error variances at long horizons are directly important. These are functions of the VARs' parameters and may be expected to have similar asymptotic properties. The author develops asymptotic theory for impulse responses and forecast error variances for VARs, ECMs and RRRs. He shows that in some cases the estimators converge to random variables (and thus are inconsistent). The paper provides detailed analysis of the modelling setups which result in inconsistency. The guiding principle to avoid it is that unit roots should be correctly specified or, at least, consistently estimated. Unrestricted VARs lead to inconsistency. Simulation results are given. They provide evidence that the developed asymptotic theory is relevant in finite samples.
forecast error variance decomposition asymptotics
scientific article; zbMATH DE number 1112375
scientific article