Mixed-frequency data Sampling Grey system Model: Forecasting annual CO emissions in China with quarterly and monthly economic-energy indicators

Global warming, mainly caused by rising carbon dioxide (CO₂) emissions in the atmosphere, has led to severe effects worldwide. Hence, reducing carbon emissions has become an urgent need to mitigate the adverse effects. To do so, accurately forecasting CO₂ emissions is crucial for policymakers in formulating climate and energy policies. Existing CO₂ emission forecast models rely on various longitudinal economy, energy or environment data collected at the same periods, e.g., yearly, as indicators. However, these data usually come from diverse sources with different sampling frequencies, e.g., monthly vs. daily. Therefore, in this paper, we introduce for the first time a Mixed-frequency data Sampling Grey system Model (MSGM) that can exploit the potential information in high-frequency sampling (HF) data of economic and social indicators to effectively forecast annual CO₂ emissions. In MSGM, (1) we directly model low-frequency CO₂ emissions and HF economic-energy influence indicators without undertaking same-frequency conversion, thereby avoiding potential information loss and enhancing prediction accuracy; (2) we introduce polynomial weight functions to address the frequency mismatch, and its parameters are obtained through search optimization algorithms; (3) unlike existing grey system models, the whitening equation of MSGM adopts a reduced-order form to address the exponential explosion issue caused by HF data accumulation; (4) the time and cumulative terms are also introduced separately to explore the effects of temporal development and historical data on future CO₂ emissions. Extensive Monte-Carlo simulations show that MSGM exhibits high accuracy on both training and testing datasets and outperforms many other state-of-the-art rival techniques like MIDAS, AR-MIDAS, AMTGM, MLRM, BPNN, SVR, ARIMA and TVGBM. We further demonstrate the potential of MSGM to forecast China's CO₂ emissions under three distinct scenarios. Out-of-sample forecasting results indicate that only under a tight-contraction scenario does the growth rate of CO₂ emissions decrease. To the best of our knowledge, the MSGM is the first technique that can exploit different frequency data to effectively forecast CO₂ emissions.