Extended dynamic mode decomposition for cyclic macroeconomic data

John Leventides; Evangelos Melas; Costas Poulios; John Leventides; Evangelos Melas; Costas Poulios

doi:10.3934/DSFE.2022006

Data Science in Finance and Economics

2022, Volume 2, Issue 2: 117-146. doi: 10.3934/DSFE.2022006

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Extended dynamic mode decomposition for cyclic macroeconomic data

Department of Economics, Faculty of Economics and Political Sciences, National and Kapodistrian University of Athens, Athens, Greece

Received: 02 April 2022 Revised: 10 May 2022 Accepted: 14 May 2022 Published: 24 May 2022
JEL Codes: E38; E37; G37; C02; C30; C60

We apply methods from the Koopman operator theory, Extended Dynamic Mode Decomposition and machine learning in the study of business cycle models. We use a simple non-linear dynamical system whose main merit is that in the appropriate parameter space sector predicts intrinsically business cycles which in the phase space are structurally stable limit cycles. Our objective is to approximate this system with a finite dimensional linear model which is defined on some augmented state space. We approximate so the trajectories of the system and obtain an alternative non-perturbative description of the system which can be used for prediction and control. This approach can also be applied to other models as well as to real data.
- business cycle,
- Samuelson-Hicks-Goodwin-Puu model,
- non-linear dynamics,
- Extended Dynamic Mode Decomposition,
- Data-driven methods,
- machine learning,
- koopman operators
Citation: John Leventides, Evangelos Melas, Costas Poulios. Extended dynamic mode decomposition for cyclic macroeconomic data[J]. Data Science in Finance and Economics, 2022, 2(2): 117-146. doi: 10.3934/DSFE.2022006

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Abstract

We apply methods from the Koopman operator theory, Extended Dynamic Mode Decomposition and machine learning in the study of business cycle models. We use a simple non-linear dynamical system whose main merit is that in the appropriate parameter space sector predicts intrinsically business cycles which in the phase space are structurally stable limit cycles. Our objective is to approximate this system with a finite dimensional linear model which is defined on some augmented state space. We approximate so the trajectories of the system and obtain an alternative non-perturbative description of the system which can be used for prediction and control. This approach can also be applied to other models as well as to real data.

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