Multi-frequency massive multi-input multi-output (MIMO) communication is a promising strategy for both 5G and future 6G systems, ensuring reliable transmission while enhancing frequency resource utilization. Statistical channel state information (CSI) has been widely adopted in multi-frequency massive MIMO transmissions to reduce overhead and improve transmission performance. In this paper, we propose efficient and accurate methods for obtaining statistical CSI in multi-frequency massive MIMO systems. First, we introduce a multi-frequency massive MIMO channel model and analyze the mapping relationship between two types of statistical CSI, namely the angular power spectrum (APS) and the spatial covariance matrix, along with their correlation across different frequency bands. Next, we propose an autoregressive (AR) method to predict the spatial covariance matrix of any frequency band based on that of another frequency band. Furthermore, we emphasize that channels across different frequency bands share similar APS characteristics. Leveraging the maximum entropy (ME) criterion, we develop a low-complexity algorithm for high-resolution APS estimation. Simulation results validate the effectiveness of the AR-based covariance prediction method and demonstrate the high-resolution estimation capability of the ME-based approach. Furthermore, we demonstrate the effectiveness of multi-frequency cooperative transmission by applying the proposed methods to obtain statistical CSI from low-frequency bands and utilizing it for high-frequency channel transmission. This approach significantly enhances high-frequency transmission performance while effectively reducing system overhead.