In recent years, a series of environmental problems have come one after another under the use of traditional fossil energy, such as greenhouse effect, acid rain, haze and so on. In order to solve the environmental problems and achieve sustainable development, seeking alternative resources has become the direction of joint efforts of China and the world. As an important part of new energy, wind energy needs strong wind speed prediction support in terms of providing stable electric power. As a result, it is very important to improve the accuracy of wind speed prediction. In view of this, this paper proposes a signal processing method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) combined with singular value decomposition (SVD), and uses Elman neural network optimized by particle swarm optimization algorithm (PSO) and autoregressive integrated moving average model (ARIMA) to predict the intrinsic mode functions (IMFs). Firstly, CEEMDAN combined with SVD is used to decompose and denoise the data, and the weights and thresholds of Elman are optimized by PSO. Finally, the optimized Elman and ARIMA are used to respectively predict the processed wind speed data components, and then the final prediction results are obtained. The final prediction results show that the proposed model can improve the effect of wind speed prediction, reduce the prediction error, and provide strong support for the stable operation of wind farms and the grid connection of power plants.