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

John Leventides; Evangelos Melas; Costas Poulios; Paraskevi Boufounou; John Leventides; Evangelos Melas; Costas Poulios; Paraskevi Boufounou

doi:10.3934/DSFE.2022021

Data Science in Finance and Economics

2022, Volume 2, Issue 4: 416-436. doi: 10.3934/DSFE.2022021

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Research article Special Issues

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

Department of Economics, Faculty of Economics and Political Sciences, National and Kapodistrian University of Athens, 1, Sofokleous str. 10559, Athens, Greece

Received: 30 September 2022 Revised: 09 November 2022 Accepted: 13 November 2022 Published: 21 November 2022
JEL Codes: C30; G17; C58; C63; C45

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.
- chaotic economic growth models,
- Koopman operators,
- EDMD,
- Takens' theorem,
- machine learning,
- finance
Citation: John Leventides, Evangelos Melas, Costas Poulios, Paraskevi Boufounou. Analysis of chaotic economic models through Koopman operators, EDMD, Takens' theorem and Machine Learning[J]. Data Science in Finance and Economics, 2022, 2(4): 416-436. doi: 10.3934/DSFE.2022021

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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.

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