Linear and nonlinear framework for interval-valued PM2.5 concentration forecasting based on multi-factor interval division strategy and bivariate empirical mode decomposition

To forecast possible air pollution risks, a large number of models have been built to predict the daily average or hourly value of PM concentrations. In fact, due to the complexity of PM formation and the diversity of its influencing factors, PM concentrations may fluctuate greatly during a certain period, single-valued methods cannot present this uncertainty and variability. Therefore, this paper develops a hybrid modeling framework that combines the elastic net (EN) and multivariate relevance vector machine (MVRVM) for interval-valued PM time series (IPMTS) forecasting. Following the philosophy of the “linear and nonlinear” modeling framework, the EN and MVRVM are applied to capture the linear and nonlinear patterns hidden in the IPMTS. Different from existing studies that directly model linear and nonlinear patterns of time series, we introduce the multi-factor interval division (MFID) strategy and bivariate empirical mode decomposition (BEMD) algorithm into linear and nonlinear pattern modeling, respectively. This enhanced linear and nonlinear framework (termed MFID-EN-BEMD-MVRVM) can consider the possible linear relationship between PM and its related factors within the intervals and model the nonlinear pattern of IPMTS at multiple scales. The IPMTS extracted from four municipalities in China are used to validate the efficiency of the proposed model. Experimental results show that the MFID-EN-BEMD-MVRVM model achieves better forecasting performance than some benchmarks and state-of-the-art models in terms of comprehensive evaluation criteria. In addition, from the application analysis, the proposed interval-valued PM modeling architecture has the possibility of real-time forecasting.