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arXiv · 2108.08461

The Bootstrap for Dynamical Systems

Kasun Fernando·Nan Zou
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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.

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Kasun Fernando, Nan Zou. 2021-08-19. The Bootstrap for Dynamical Systems. https://arxiv.org/abs/2108.08461

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