A Generalization of the Grey Lotka–Volterra Model and Application to GDP, Export, Import and Investment for the European Union

Abstract

This study proposes a generalized grey Lotka–Volterra model with a finite number of variables. The model is obtained by applying the grey modelling method to estimate the parameters of a finite dimensional quadratic Lotka–Volterra system. Subsequently, the model is used to analyze the competition and cooperation relationship between four macroeconomic indicators, namely Gross Domestic Product, Export, Import and Investment, and to obtain short-time forecasting for them. The data used in the empirical investigation cover the time periods 2005–2022 and 2011–2022, for the European Union. The empirical results are compared to the ones obtained by using the grey model GM(1,1) and the two-dimensional grey Lotka–Volterra model. Finally, economic interpretations of the empirical findings are formulated.

Keywords

• grey model
• generalized grey Lotka–Volterra model
• gross domestic product
• export
• import
• investment