Extended dynamic mode decomposition for cyclic macroeconomic data

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.

Keywords

• business cycle
• samuelson-hicks-goodwin-puu model
• non-linear dynamics
• extended dynamic mode decomposition
• data-driven methods
• machine learning
• koopman operators