The prediction of nonlinear and non-stationary systems is a research topic of great scientific significance. In some recent work the convergent cross mapping (CCM) algorithm is used to detect the causal relationship between variables. In the CCM algorithm, the points close to each other in the phase space have similar trends and trajectories in time. Therefore, this method can be applied to the prediction of experimental researches of nonlinear and non-stationary systems. Therefore, in this paper the CCM algorithm is applied to the prediction of the Lorenz system and the actual climate time series, and the effects of different phase space reconstruction methods on the prediction skill are investigated. The preliminary results are as follows. 1) No matter whether the ideal Lorenz model or the actual climate series, of the three reconstruction phase space methods of univariate, multivariate, and multiview embedding method, the multiview embedding method is the best predictive skill, indicating that for a given length of time series, the more the information contained in the reconstructed phase space, the stronger its predictive ability is. 2) Adding the data of NAM (northern hemisphere annular mode) to the reconstructed phase space of SAT (surface air temperature) can improve the prediction effect on prediction of SAT. Using the univariable, multivariable, and multiview embedding method for implementing prediction, the characteristics of common information in the complex system are considered. On condition that the length of the time series is fixed, the complexity of the dynamic system can be used to increase the information of the system. Based on causality detection, through the extraction of quantitative information of data, a novel idea for the improvement of predictive skills in nonlinear and non-stationary systems can be obtained.