Exploiting PSO-SVM and sample entropy in BEMD for the prediction of interval-valued time series and its application to daily PM2.5 concentration forecasting

In view of the serious harm to human health caused by atmospheric fine particulate matter (PM2.5), accurate prediction of high concentrations of PM2.5 can help to provide timely warnings. On the other hand, due to the complexity of the formation and transmission process, it is difficult to accurately predict PM2.5. The aim of this paper is to develop a hybrid interval-valued time series prediction model, namely, BEMDCR-SE-PSO-SVM, by considering daily changes in pollutant concentrations and thereby realize interval-valued PM2.5 concentration prediction with high accuracy. The theoretical contributions in this paper include (1) the problem of edge effects corresponding to BEMD associated with interval-valued time-series is addressed by using the mirror extension method, and (2) the transformation between interval-valued time series and complex-valued signals is renewed from the perspective of centre/radius so that lower data fluctuations can be obtained. Technologically, sample entropy is introduced to provide an objective way to integrate decomposed similar IMFs so that subsequent prediction processes can be simplified. Finally, a numerical example is shown to illustrate the feasibility and validity of the developed hybrid interval-valued time series prediction model.