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

TL;DR

This paper uses a global modelling approach to identify a chaotic attractor in economic data, revealing complex dynamics and a unique topological feature with an additional branch, linking economic variables like exchange rate, unemployment, and inflation.

Contribution

It introduces a novel chaotic attractor model derived from economic data and analyzes its topological structure, highlighting an additional branch in the attractor's return map.

Findings

Chaotic dynamics are present in economic data.

The model links exchange rate, unemployment, and inflation.

An additional branch in the attractor's topology is identified and interpreted.

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 Poincar\'e section. Consequences of this particular structure are analysed and interpreted economically.