The Bootstrap for Dynamical Systems

TL;DR

This paper develops a bootstrap method tailored for dynamical systems, establishing its consistency and efficiency through novel continuous Edgeworth expansions, and verifies these results with simulations.

Contribution

It introduces the first continuous Edgeworth expansion for dynamical systems and applies bootstrap techniques to estimate parameter uncertainty.

Findings

Bootstrap for dynamical systems is consistent and efficient.

First continuous Edgeworth expansion for dynamical systems.

Simulation confirms theoretical results.

Abstract

Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using statistical methods. When measuring the uncertainty of such parameter estimation, the bootstrap stands out as a simple but powerful technique. In this paper, we develop the bootstrap for dynamical systems and establish not only its consistency but also its second-order efficiency via a novel \textit{continuous} Edgeworth expansion for dynamical systems. This is the first time such continuous Edgeworth expansions have been studied. Moreover, we verify the theoretical results about the bootstrap using computer simulations.