Determining the chaotic behaviour of copper prices in the long-term using annual price data

Mineral commodity prices are influenced by economic, technological, psychological, and geopolitical factors. Stochastic approaches, and time series and econometric techniques have been used to represent the dynamics of mineral commodity markets and predict prices. However, these techniques cannot provide a comprehensive representation of market dynamics because they do not recognise the relationship between these factors over time, and they are unable to capture both the evolution and the cumulative effects of these factors on prices. Stability of motion and chaos theories can detect sensitivity to initial conditions, and therefore the evolutionary patterns allowing a proper understanding and representation of mineral commodity market dynamics. Most of the techniques used to assess chaos require a colossal amount of data, so the use of small data sets to assess chaos has been largely criticised. Nevertheless, by definition, the dynamics of a chaotic system remain at different scales owing to its self-organisation features that exhibit ordered patterns in the absence of codes or rules. Therefore, any deterministic chaotic behaviour of mineral commodity prices can be captured by using small data sets if a detailed qualitative and quantitative analysis are carried out. This paper examines the chaotic behaviour of annual copper prices between 1900 and 2015. To do so, we combine chaos theory, stability of motion and statistical techniques to reconstruct the long-term dynamics of copper prices. First, we examine the time dependency and the presence of a strange attractor by a visual analysis of the time series and phase space reconstruction based on Takens’ theorem and determine embedding parameters. Then we examine the dynamic characteristics of the system which assesses its complexity and regularity patterns to measure the system’s entropy. Finally, we calculate the largest Lyapunov exponent λ to assess the sensitivity to initial conditions and determine chaotic behaviour supported by a surrogate test. We find that annual copper prices have a chaotic behaviour embedded in a high-dimensional space and short time delay. The study suggests that copper prices exhibit only a single state of low prices, which fluctuate through transitional periods of high prices. It challenges the assertion that metal markets have fluctuated over four major super cycles and debate the adequacy of stochastic and econometric models for representing mineral commodity market behaviour. This study recommends that the use of chaotic behaviour improves our understanding of mineral commodity markets and narrows the data searching, processing and monitoring requirements for forecasting. Therefore, it improves the performance of traditional techniques for selecting key factors that influence the market dynamics, and may also be used to select the most suitable algorithm for forecasting prices.