Non-parametric Estimation of Deterministically Chaotic Systems.

This paper studies theoretical and econometric issues that arise in systems characterized by deterministic chaos. Such systems can arise from standard dynamic economic models and are extensively used in Monte Carlo and other simulation-based statistical procedures which use pseudo-random number generators. The virtues of studying chaotic laws of motion in the space of densities over the state space are shown. A complete characterization of deterministic stationary ergodic processes in that space of densities is suggested.and proved when the invariant measure is unknown. The asymptotic properties of the kernel estimators of the stationary density and the law of motion in the density space studied, and shown to hold for chaotic systems. Small sample behavior for the estimators is subjectively shown to be good even when optimal choices of the kernel and smoothing parameters are not exploited.