Studying the characteristics of wind speed is essential in wind speed prediction. Based on long-term observed wind speed data, fractal dimension analysis of wind speed was first conducted at different scales, and persistence in wind speed was evaluated based on fractal dimensions in this paper. To propose a more accurate model for wind speed prediction, the wavelet decomposition method was applied to separate the high-frequency dynamics of wind speed data from the low-frequency dynamics. Chaotic behaviors were studied for each decomposed component using the largest Lyapunov exponents method. A proposed hybrid prediction method combining wavelet decomposition, a chaotic prediction method and a Kalman filter method was investigated for short-term wind speed prediction. Simulation results showed that the proposed method can significantly improve prediction accuracy.