Accurately predicting quarterly or monthly energy consumption remains challenging so far. Despite the abundance of relevant studies, most of them focus on univariate modeling. Moreover, the core of nearly all multivariate forecasting studies is an unstable forecasting system based on a single model. Therefore, there is an urgent need for an efficient and rational prediction method. For the prediction task of quarterly or monthly energy consumption characterized by small samples and nonlinearity, this article develops a new joint forecasting-centered forecasting framework by integrating machine learning and grey system theory. In this forecasting framework, grey relational analysis is used to filter the influencing factors of the study object, a new adaptive weighted least squares support vector regression model is developed to describe the relationship between the study object and the filtered influencing factors, and a new difference equation prediction model is employed to predict the future values of the filtered influencing factors. The joint forecasting task is accomplished by inputting the future values of the filtered influencing factors into the trained adaptive weighted least squares support vector regression model. Experimental simulation results demonstrate that the two prediction models developed in this framework, along with the overall forecasting approach, outperform competing methods. These results confirm the effectiveness of the proposed forecasting framework in accurately predicting quarterly or monthly energy consumption, even in scenarios with limited data and nonlinear relationships.