IMPULSE-RESPONSE AND FORECAST ERROR VARIANCE ASYMPTOTICS IN NONSTATIONARY VARS

Estimated impulse responses and forecast error decompositions are show n to be inconsistent at long horizons in unrestricted VARs with some u nit roots. Predictions from unrestricted VARs also do not converge to the optimal predictors over long forecast horizons. In contrast, reduc ed rank regressions produce impulse responses and forecast error varia nce estimates that are consistent and predictions that are asymptotica lly optimal, provided the cointegrating rank is correctly specified or consistently estimated by an order selector such as PIG. Some simulat ions show these findings to be relevant in finite samples in VARs with some unit roots and cointegration. (C) 1998 Elsevier Science S.A.