Nonparametric estimation of generalized impulse response function - Rolf Tschernig; Lijian Yang (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2000)
A local linear estimator of generalized impulse response (GIR) functions for nonlinear conditional heteroskedastic autoregressive processes is derived and shown to be asymptotically normal. A plug-in bandwidth is obtained that minimizes the asymptotical mean squared error of the GIR estimator. A local linear estimator for the conditional variance function is proposed which has simpler bias than the standard estimator. This is achieved by appropriately eliminating the conditional mean. Alternatively to the direct local linear estimators of the k-step prediction functions which enter the GIR estimator the use of multi-stage prediction techniques is suggested. Simulation experiments show the latter estimator to perform best. For quarterly data of the West German real GNP it is found that the size of generalized impulse response functions varies across different histories , a feature which cannot be captured by linear models.
urn:nbn:de:kobv:11-10048150
Keywords: 330; Confidence intervals; general impulse response function; heteroskedasticity; local polynomial; multi-stage predictor; nonlinear autoregression; plug-in bandwidth.