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Interval-valued time series (ITS) has been widely concerned by the academic community due to its outstanding performance in dealing with the uncertainty of systems. Numerous ITS forecasting studies have emerged, while the most popular method is based on "divide and conquer". For ITS analysis, bivariate empirical mode decomposition (BEMD) is currently the main tool that can simultaneously consider the interrelationships between the upper and lower limits. The concern is that, like empirical mode decomposition (EMD), BEMD suffers from mode mixing and end-point effects, which leads to unsatisfactory results of decomposition. In this paper, a bivariate ensemble empirical mode decomposition (BEEMD) method is proposed and applied to ITS forecasting, which aims at alleviating the problems mentioned above. At the same time, dynamic time warping (DTW) is used to quantize and analyze the mode mixing. Then, the effects of complex-valued signal constructions on ITS forecasting are discussed. To overcome the uncertainty and instability that may arise from a single prediction method, an optimal prediction based on the model pool is designed for sub-modes, and the final result can be obtained by simple addition. Using carbon prices, West Texas Intermediate (WTI) crude oil prices, and short-term loads, as the research objects, the results indicate that BEEMD is effective in avoiding mode mixing in BEMD, the complex-valued signal construction based on center and radius method (CRM) is more conducive to forecasting and optimal prediction can further improve forecasting accuracy. [ABSTRACT FROM AUTHOR]