Purpose: This paper applied grey wave forecasting in a decomposition–ensemble forecasting method for modelling the complex and non-linear features in time series data. This application aims to test the advantages of grey wave forecasting method in predicting time series with periodic fluctuations.Design/methodology/approach: The decomposition–ensemble method combines empirical mode decomposition (EMD), component reconstruction technology and grey wave forecasting. More specifically, EMD is used to decompose time series data into different intrinsic mode function (IMF) components in the first step. Permutation entropy and the average of each IMF are checked for component reconstruction. Then the grey wave forecasting model or ARMA is used to predict each IMF according to the characters of each IMF.Findings: In the empirical analysis, the China container freight index (CCFI) is applied in checking prediction performance. Using two different time periods, the results show that the proposed method performs better than random walk and ARMA in multi-step-ahead prediction.Originality/value: The decomposition–ensemble method based on EMD and grey wave forecasting model expands the application area of the grey system theory and graphic forecasting method. Grey wave forecasting performs better for data set with periodic fluctuations. Forecasting CCFI assists practitioners in the shipping industry in decision-making.