A novel three-stage hybrid learning paradigm based on a multi-decomposition strategy, optimized relevance vector machine, and error correction for multi-step forecasting of precious metal prices

Abstract

Accurate forecasting of precious metal prices will greatly assist investors, account managers, and mineral enterprises in making sound decisions and market assessments, while further improvement in the accuracy of precious metal price forecasting is challenging due to its non-linear oscillating characteristics. This paper proposes a novel three-stage hybrid learning paradigm for accurately predicting the prices of three precious metals, i.e., silver, palladium, and platinum. Firstly, the original price series will be decomposed by the complementary ensemble empirical mode decomposition (CEEMD) into several subsequences. Then the subsequences are reprocessed by secondary decomposition (SD) and sequence reconstruction using WPD and permutation entropy to reduce data noise and repetitive modeling. Secondly, all subsequences are fed into the relevance vector machine improved by the African vulture optimization algorithm for prediction to obtain the initial prediction results and the error series. Finally, the error series is further decomposed and predicted by WPD and an optimized relevance vector machine to correct the previously predicted precious metal prices and obtain the final prediction results. The actual precious metal price data are provided as model inputs for multi-step ahead forecasting, and the experimental results show that: the proposed novel learning paradigm achieves MAPE values of 0.2003%, 0.4552%, and 0.2151% for one-step-ahead forecasting of the prices of silver, palladium, and platinum, respectively; the proposed hybrid model performs the best among all the compared models, where hybridization of all the components is essential to improve the prediction accuracy and enables the proposed model to have a higher generalization capability; the results of this paper may provide more scientific insight and reference for precious metals investment and production.