Topological characterisation of a chaotic attractor with an additional branch generated from economic data

Abstract

There are insights of chaotic properties in economic systems and data. To prove the existence of chaotic dynamics, the establishment of a deterministic model is mandatory. A global modelling tool (GPoM) is used to search for mathematical models of equations from economic data: unemployment, inflation and nominal exchange rate over 30 years. A system of three differential equations is chosen as a model, whose solution is a chaotic attractor in $\mathbb{R}^3$. The model extracted from the data is not able to fit them, but it provides equations linking those multiple economic variables and reveals significant impact of exchange rate on unemployment and inflation evolution. The topological characterisation of the chaotic attractor solution exhibits an additional branch in its first return map to the Poincaré section. Consequences of this particular structure are analysed and interpreted economically.