Whether Uncertainty Theory Can Enhance GDP Forecasting From Energy: A New Uncertain MIDAS Model

In response to the potential failure of traditional models when faced with issues of nonwhite noise residuals and imprecise data, this study extends the mixed data sampling (MIDAS) model to the field of uncertainty theory to tackle these challenges. Under the framework of uncertainty theory, this research addresses the frequency inconsistency in economic data collection by constructing two types of uncertain MIDAS models, aiming to fill the gap in uncertainty theory's handling of predictive analysis for variables with different frequencies. Furthermore, this study integrates the dual perspectives of energy consumption and energy‐related carbon dioxide emissions. By building uncertain MIDAS models with uncertain disturbance terms and traditional MIDAS models, the research systematically establishes and comparatively analyzes univariate and multivariate energy consumption, departmental carbon dioxide emissions, and multivariate models that combine these two perspectives. The study's results not only confirm the nonwhite noise characteristics of residuals and validate the rationality of treating residuals as uncertain disturbance terms but also demonstrate through comparative analysis that the uncertain MIDAS model outperforms the traditional MIDAS model in terms of forecasting effectiveness. Moreover, the multivariate forecasting method that considers both perspectives can more comprehensively describe and predict the US quarterly gross domestic product (GDP), showing its superior predictive capability. Furthermore, by altering the evaluation criterion, substituting GDP with nominal GDP and introducing the control variables for robustness analysis, we have further verified the robustness of the model and its results.