| Summary: | With the acceleration of urbanization, there is an increasing trend of heavy pollution. PM<sub>2.5</sub>, also known as fine particulate matter, refers to particles in the atmosphere with a diameter of less than or equal to 2.5 microns. PM<sub>2.5</sub> has a serious impact on human life, a sustainable city, national economic development, and so on. How to forecast the PM<sub>2.5</sub> concentration accurately, and then formulate a scientific air pollution prevention and monitoring program is of great significance. This paper proposes a hybrid model based on echo state network (ESN) and an improved particle swarm optimization (IPSO) algorithm for the Beijing air pollution problem, and provides a method for PM<sub>2.5</sub> concentration forecasting. Firstly, the PSO algorithm is improved to speed up the search performance. Secondly, the optimal subset of the original data is selected by the convergence cross-mapping (CCM) method. Thirdly, the phase space reconstruction (PSR) process is combined with the forecasting model, and some parameters are optimized by the IPSO. Finally, the optimal variable subset is used to predict PM<sub>2.5</sub> concentration. The 11-dimensional air quality data in Beijing from January 1 to December 31, 2016 are analyzed by the proposed method. The experimental results show that the hybrid method is superior to other comparative models in several evaluation indicators, both in one-step and multi-step forecasting of PM<sub>2.5</sub> time series. The hybrid model has good application prospects in air quality forecasting and monitoring.
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