Prediction of renewable energy consumption structure (RECS) can provide important guidance for energy development planning and energy structure transformation. The RECS refer to the proportion of various renewable energy consumptions and belong to compositional data, which could reflect the structural shapes of a complete system better. The multivariate compositional data's vector autoregressive model (CDVAR) on the basis of the Simplex space and its algebraic system is proposed in this study aiming at the multi-dimensional small sample size. Firstly, the algebraic system of the Simplex space is introduced and the statistics of the compositional data are defined. Secondly, the novel model with the form of the compositional data is obtained and the least square parameter estimation of the model is derived according to Aitchison geometry. Third, the validation of the novel model is verified by the data on RECS in countries (China, USA, and Canada). The validation presents that the proposed model performs better in fitting, prediction, stability, and applicability compared with other five models under transformation. Last, the proposed model is applied to analyze and forecast the RECS of the above countries in 2021-2025 to provide an important basis for the optimization of the RECS.
