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In order to improve the accuracy of forecasting crude oil prices, a new crude oil price forecasting method is introduced in the paper that is a combination of the FNN model and the stochastic time effective function—namely, the WT-FNN model. The FNN model keeps track of the historical values of crude oil prices and predicts future crude oil prices, and the stochastic time effective function gives greater weight to recent information and smaller weight to old information, thus making the prediction of crude oil prices more reasonable. We selected the daily data of Brent crude oil prices from 4 January 2000 to 30 September 2021 as research objects and then used the WT-FNN model to train and predict the research objects. By comparing it to the benchmark model, we found that the predictive effect of the WT-FNN model was better than the FNN model and the no-change model. The results also passed a robustness test. [ABSTRACT FROM AUTHOR]