Wavelet entropy and complexity–entropy curves approach for energy commodity price predictability amid the transition to alternative energy sources

In recent years, energy commodities have emerged as pivotal and widely debated subjects, driven by their profound influence on the global economy and their intricate interconnections. Moreover, the challenges stemming from the predictability of energy commodity prices have become a prominent and intensifying focus of discussion. To this aim, in this paper, we employ wavelet analysis with an entropy approach to investigate and evaluate fluctuations, low-frequency events, and rare events in energy commodity prices and the consequent predictability of such time series. In particular, wavelet analysis can differentiate high-frequency from low-frequency movements in a time series, and entropy is a valuable mathematical tool used to evaluate the state of disorder, randomness, or uncertainty in a time series. Specifically, we employ Rényi Entropy instead of the Shannon entropy because it allows for enhanced consideration of low-frequency events and spikes in a time series. Therefore, to analyze the predictability of a series, we use Wavelet Rényi Entropy (WRE) and the Rényi complexity–entropy curves by combining the wavelet transform with Rényi entropy. Finally, we apply our analysis to real financial data, including energy commodities and indices that can describe the transition to alternative energy resources.