Using entropy to assess dynamic behaviour of long-term copper price

Abstract

Since mineral commodities have considerable commercial significance, many techniques have been developed to forecast their prices. Some of these techniques assume that price fluctuations follow well-known cycles or that they have random origins. Many studies have claimed that prices of certain mineral commodities, such as copper, exhibit long-term cyclical behaviour. This is questionable, because while events in mineral commodity markets may repeat in the same order, they are far from being regular, as it is unlikely that they recur at the same intervals and intensity. On the other hand, the assertion of stochastic behaviour seems improbable as it is known that markets are driven by the human decision-making process that, according to neuroscience and psychology disciplines, is based on the learning and cognitive capacities of humans. Moreover, in the last decade, it has been claimed that mineral commodity prices exhibit chaotic behaviour. This paper aims to expand the understanding of mineral commodity prices behaviour in the long-term which will improve forecasting models. We do this by introducing a set of nonlinear dynamic tests largely used in human-related fields, medicine and economics. The assessment encompasses Approximate Entropy (ApEn), Sample Entropy (SampEn), surrogate analysis and False Nearest Neighbour (FNN) test. Copper is used as a case study because it is considered one of the most competitive, strategic and representative mineral commodities traded on the stock exchanges worldwide. The study further examines the long-term dynamics of annual price represented by a data set of 116 observations of average yearly values between 1900 and 2015. It reveals that long-term copper prices do not behave periodically, but exhibit patterns like chaotic time-related systems which debate the classical assertion of cyclicality. It was also found that long-term copper price time series is nonlinear, non-Gaussian, and has dynamic deterministic behaviour, which cannot be generated by a stochastic process.