Analysis of chaotic economic models through Koopman operators, EDMD, Takens' theorem and Machine Learning

Abstract

We consider dynamical systems that have emerged in financial studies and exhibit chaotic behaviour. The main purpose is to develop a data-based method for reconstruction of the trajectories of these systems. This methodology can then be used for prediction and control and it can also be utilized even if the dynamics of the system are unknown. To this end, we combine merits from Koopman operator theory, Extended Dynamic Mode Decomposition and Takens' embedding theorem. The result is a linear autoregressive model whose trajectories approximate the orbits of the original system. Finally, we enrich this method with machine learning techniques that can be used to train the autoregressive model.

Keywords

• chaotic economic growth models
• koopman operators
• edmd
• takens' theorem
• machine learning
• finance