# Integrated Predictor Based on Decomposition Mechanism for PM2.5 Long-Term Prediction
## 1 Introduction
However, the RNN structure encounters gradient disappearance and gradient explosion during network training, and it is difficult to perform multi-step optimization training. Hence, three gates were added based on RNN, and the long short-term memory (LSTM) network was proposed to solve the long-term dependence of a RNN [25]. A gated recurrent unit (GRU) network, with two gating structures, was proposed based on LSTM [26], and it could achieve the same, or even better, performance. Recently, the deep-learning methods employed for air-pollution prediction have attracted wide interest among researchers. For example, the deep regression neural network (DRNN) [27] approach was proposed to predict the daily air-quality classification (AQC). [PERSON] and [PERSON] [28] used a hybrid model based on convolutional neural networks (CNNs) and LSTM to predict PM2.5 concentrations one hour in advance. The results showed that the proposed model outperformed the machine-learning algorithms such as support vector machine, random forest, and multilayer perceptron. [PERSON] et al. [29] used a CNN plus LSTM based on spatio-temporal data to obtain 1-d-ahead prediction with high performance. Until now, researchers have agreed that deep-learning networks are the most powerful in nonlinear modeling. However, the above research results are based on short-term forecasts. [PERSON] et al. [29] gave a next-day prediction, but the data they used were the average concentration of PM2.5 per day, so the predicted result did not show the hourly variation of the next day. Therefore, from the perspective of a prediction problem, it is also a short-term prediction. However, long-term forecasts are very meaningful, especially for the management of air quality. For example, the model of [PERSON] et al. [3] is based on the concentration of PM2.5 per hour, giving the concentration of PM2.5 per hour for the next 10 h. Compared with [29], which only gives the average of the next day, [PERSON]'s method [3] can provide more detailed information to guide people's lives and travel. We note that the current weather forecast information also gives the concentration of PM2.5 per hour for the next 24 h.  
In this study, an attempt was made to improve the long-term prediction accuracy of PM2.5 on the basis of a deep-learning network. We found that the deep-learning network has a weak ability to model linear data, especially for the prediction problem of time-series data. PM2.5 data do have a linear component, which is the reason why the long-term prediction performance of deep neural networks will decline. In general, PM2.5 time-series data contain three components:  
1. Trend component: This refers to the main trend direction of PM2.5 time-series data. This part often includes the trend of linear growth and decline. The trend component in PM2.5 data reflects the pollution of weather over a long period of time. If there are negative effects such as industrial pollution and automobile exhaust, the trend component of PM2.5 will exhibit linear growth. Conversely, if the air quality improves, the trend component of PM2.5 data will slowly decrease. 2. Period component: This refers to the data fluctuation that occurs repeatedly over a period of time. We found that the PM2.5 data had obvious period characteristics in one day; that is, the value during the day is higher and is lower than at night. 3. Residual component: This refers to the remaining part of the original data minus the trend and period components, and usually consists of complex nonlinear element and noise. Figure 1 is an example of hourly PM2.5 average concentration data from January to February 2016 in Beijing, China, from which it can be seen that the trend in this period is upward from 40 \(\mathrm{\SIUnitSymbolMicro g}\mathrm{/}\mathrm{m}^{3}\) to nearly 50 \(\mathrm{\SIUnitSymbolMicro g}\mathrm{/}\mathrm{m}^{3}\). We know that Beijing is a northern city, and the winter season in Beijing from January to February is the heating season.