# Integrated Predictor Based on Decomposition Mechanism for PM2.5 Long-Term Prediction
## 1 Introduction  
Air quality has had a huge impact on human health and climate, so the effective management of air quality and its accurate assessment and prediction have received widespread attention in recent years. As one of the important air quality indices (AQIs), the prediction of PM2.5 concentration is a necessary evaluation parameter for air quality forecast [1, 2]. It is difficult to obtain an accurate long-term prediction of PM2.5 concentration because PM2.5 comprises typical complex nonlinear time-series data [3], where the vector field of state dynamics is a nonlinear function of state variables. In the literature, the estimation and prediction of air quality are often based on mathematical models, the predicted models can be established through some parameter estimation methods [4, 5, 6, 7], some have used input-output representations [8, 9, 10, 11], and others have used state-space models [12, 13]. The methods used to realize accurate and efficient prediction of complex time-series data include traditional time-series modeling methods, shallow networks based on machine learning, and deep-learning networks. Traditional methods predict the future trend of PM2.5 based on a statistical model of historical data including autoregressive-integrated moving average (ARIMA)models [14] and vector auto-regression (VAR) [15]. ARIMA is a linear modeling method that provides accurate predictions for approximate linear relationships. However, its prediction performance is not good enough for nonlinear prediction problems. To capture the complex nonlinearity of PM2.5, a back propagation (BP) neural network has been widely applied in time-series data prediction [16; 17; 18]. Other shallow nonlinear networks based on a machine-learning mechanism such as the improved gray neural network model [19] and the radial basis function (RBF) neural network [20] have also been used to predict time-series data. [PERSON] et al. [3] proposed a supplementary leaky integrator echo state network (SLI-ESN), which added the historical state term of the historical moment to the calculation of a leaky integrator reservoir. Compared with an echo state network (ESN), a leaky integrator ESN (LI-ESN), an extreme learning machine (ELM), a hierarchical ELM (H-ELM), a stacked auto-encoder (SAE), and a traditional SLI-ESN, the proposed SLI-ESN of [PERSON] et al. [3] could achieve good prediction results, but its long-term predictions were not satisfactory. As a shallow network still cannot effectively extract the complex nonlinearity of the data, decomposition must be used; that is, the data must be decomposed into multiple components to reduce its complexity, and then multiple sub-models are used to improve the prediction performance. For example, [PERSON] et al. [21] decomposed a long-term data series into smaller seasonal component patterns. [PERSON] et al. [22] divided a pollen-concentration data series into seasonal and random parts, used partial least-squares regression (PLSR) to fit the residuals, and established an airborne pollen time-series model to predict the daily pollen concentration. [PERSON] et al. [23] extracted accurate seasonal signals, and used maximum likelihood estimation (MLE) to estimate the long-term trend of the seasonally adjusted time series, which improved the prediction accuracy of the data. We note that the use of these decomposition methods compensates the nonlinear modeling capabilities of shallow networks. The original time-series data are decomposed into multiple sub-sequences, and the degree of nonlinearity of each sub-sequence is reduced. Therefore, for each sub-sequence, the training process of shallow network parameters is easier to converge, and the loss function of the training is smaller, so the obtained model is more accurate, and the prediction performance improved. To improve the ability to model nonlinearities, deep neural networks have made great progress in regression prediction in recent years, especially the regression deep-learning network represented by a recurrent neural network (RNN) [24].