Multi-step prediction for nonlinear autoregressive models based on empirical distributions

Abstract

A multi-step prediction procedure for nonlinear autoregressive (NLAR) models based on empirical distributions is proposed. Calculations involved in this prediction scheme are rather simple. It is shown that the proposed predictors are asymptotically equivalent to the exact least squares multi-step predictors, which are computable only when the innovation distribution has a simple known form. Simulation studies are conducted for two- and three-step predictors of two NLAR models.