Pigeon-inspired optimization and extreme learning machine via wavelet packet analysis for predicting bulk commodity futures prices

In this paper, a hybrid approach consisting of pigeon-inspired optimization(PIO) and extreme learning machine(ELM) based on wavelet packet analysis(WPA) is presented for predicting bulk commodity futures prices. Firstly, WPA is applied to decompose the original futures prices into a set of lower-frequency subseries. Secondly, the PIO algorithm is used to optimize the parameters of ELM and then the optimized ELM is utilized to forecast the subseries. Finally, we adopt the hybrid method to calculate the final forecasting outcomes of futures prices. In order to further test the predictive ability of the hybrid forecasting model on bulk commodity futures prices, we use the prices of West Texas Intermediate crude oil futures and Chicago Board of Trade soybean futures to make one-step, two-step and four-step ahead predictions. In comparison with complete ensemble empirical mode decomposition with adaptive noise, empirical mode decomposition and singular spectrum analysis, WPA is the most suitable for decomposing bulk commodity futures prices.The experimental outcomes show that the hybrid WPA-PIO-ELM model has better performance on horizontal precision, directional precision and robustness.