Notice of Retraction Effects simulation of international natural gas prices on crude oil prices based on WBNNK model

International crude oil prices are very complex nonlinear time series, which are not only affected by the domination of objective economic laws, but also by politics and pricing system. Therefore it is difficult to establish an effective prediction model based on the general time series analysis. So we need to understand the effects of international natural gas prices on crude oil prices to get more accuracy prediction of crude oil prices. In this paper, we build up WBNNK (wavelet-based Boltzmann cooperative neural network and kernel density estimation) model. The international natural gas ad crude oil prices time series is decomposed into approximate components and random components. International natural gas prices could affect the entire world pricing system. The approximate components, which represented the trend of oil price, are predicted with Boltzmann neural network, which is cooperative with international natural gas prices; the random components are predicted with Gaussian kernel density estimation model. In this paper, we analyzed the time-frequency structure of dubieties wavelet transform coefficient modulus for crude oil price time series, and predicted the oil price with Boltzmann neural network and Gaussian kernel density estimation model. The results show that the model has higher prediction accuracy.