Wavelet transform (WT), as a data preprocessing algorithm, has been widely applied in electricity price forecasting. However, this deterministic-based algorithm does not present stable performance owing to the experiential selection of its orders and layers. For determining the selection of WT’s orders and layers in U.S. electricity prices forecasting, this paper designs a crossover experiment with 240 schemes of WT parameter selection and forecasts each scheme with stacked autoencoder (SAE) and long short-term memory (LSTM), generating a novel hybrid model WT-SAE-LSTM. The results show that the proposed model outperforms other AI models, such as back propagation neural network et al., in forecasting accuracy. The best performance of WT-SAE-LSTM in residential, commercial, and industrial electricity price cases obtained by five order four layers, five order four layers, and four order seven layers, where the MAPE is 0.8606%, 0.4719%, and 0.4956%, respectively. Additionally, the difference between the proposed forecasting model and the forecasting result of Energy Information Administration (U.S.) is small. This paper determines the optimal orders and layers of WT in U.S. electricity prices forecasting, which provides an effective reference for the application of WT in other forecasting scenarios and for electricity market participants. •WT-SAE-LSTM is proposed to forecast electricity prices of U.S.•SAE-LSTM has better forecasting accuracy.•The optimal wavelet’s orders and layers are determined.•WT-SAE-LSTM has practical application value.