Major nations across the globe are increasingly concerned about the rising trends in carbon dioxide (CO2) emissions, particularly in societies of varying scales. Against this backdrop, precise prediction of carbon emissions becomes critically important, especially for the formulation and adjustment of near-term carbon reduction policies. However, the non-linear, non-stationary, and complex nature of daily carbon emission data poses a great challenge for daily-level forecasting especially in the big data context. To address this issue, we propose a novel composite forecasting approach named DCEF dedicated to the estimation of daily carbon emissions. In concrete, our approach employs the Empirical Mode Decomposition (EMD) for data stabilization and the Auto-regressive Integrated Moving Average (ARIMA) model for forecasting, while integrating the Truncated singular value decomposition(TSVD) technique for data compression and mitigating noise. Finally, DCEF is empirically validated with real daily carbon emission datasets collected from 6 sectors in 13 countries of varying sizes. Experimental results demonstrate the advantages of our approach compared to other baseline models in terms of prediction accuracy and efficiency.