Predictors in Dynamic Nonlinear Models: Large-Sample Behavior

Abstract

The large-sample behavior of one-period-ahead and multiperiod-ahead predictors for a dynamic nonlinear simultaneous system is examined in this paper. Conditional on final values of the endogenous variables, the asymptotic moments of the deterministic, closed-form, Monte Carlo stochastic, and several variations of the residual-based stochastic predictor are analyzed. For one-period-ahead prediction, the results closely parallel our previous findings for static nonlinear systems. For multiperiod-ahead prediction similar results hold, except that the effective number of sample-period residuals available for use with the residual-based predictor is T/m, where T denotes sample size. In an attempt to avoid the problems associated with sample splitting, the complete enumeration predictor is proposed which is a multiperiod-ahead generalization of the one-period-ahead residual-based predictor. A bootstrap predictor is also introduced which is similar to the multiperiod-ahead Monte Carlo except disturbance proxies are drawn from the empirical distribution of the residuals. The bootstrap predictor is found to be asymptotically inefficient relative to both the complete enumeration and Monte Carlo predictors.