## 2 Materials and Methods
### Method
#### 2.3.3 SARIMA Model  
Generally, historical data will have a strong relationship at the potential cycle time points, especially in economics. The SARIMA model is mainly used to identify the predictions of dependent variables, influenced by seasonal fluctuations and external events. The SARIMA model contains trend and seasonal variation, which has been widely used in different fields, such as economics, statistics, and RS, forecasting a certain parameter in time series with seasonality [30; 31; 32; 33]. According to the definition, the SARIMA model is generally referred to SARIMA \(\left(p,d,q\right)\times\left(P,D,Q\right)_{s}\). Where \(d\) and \(D\) are the order of the stepwise difference and the seasonal difference, respectively; \(p\) and \(q\) are the order of autoregressive and moving average, respectively; \(P\) and \(Q\) are the order of seasonal autoregressive and seasonal moving average, respectively; \(S\) is the seasonal period. The model can be expressed as follows:  
\[\phi_{p}(B)\Phi_{P}(B^{S})(1-B)^{d}(1-B^{S})^{D}y_{t}=\theta_{q}(B)\Theta_{Q}( B^{S})a_{t} \tag{8}\]  
where,  
\[\begin{array}{l}\phi_{p}(B)=1-\phi_{1}B-\phi_{2}B^{2}-\cdots-\phi_{p}B^{p}\\ \theta_{q}(B)=1+\theta_{1}B+\theta_{2}B^{2}+\cdots+\theta_  
The general matching process includes three steps: identification, estimation, and diagnostic checking. The crucial step in the SARIMA model is the choice of orders. The main methods used are autocorrelation functions (ACF) and partial autocorrelation functions (PACF), Akaike's information criterion (AIC), and so on. First, we used the ACF and PACF methods to select several possible orders. After modeling, the AIC criterion was used to select the best order model. The \(p\) value in the model was taken as 1, and the D value was taken as 1. After the model was established, it needed to be tested. The method used here is the residual ACF test. In model testing, we are mainly concerned about whether the residual of the model is relevant, and normally distributed with a mean of zero. If the residuals of the SARIMA model are correlated and not normally distributed with a mean of zero, then the model can be further improved. On the contrary, the model fitting effect is good, and it can be considered that the model fully extracts the information of the sequence. For the test of residual white noise, LB test was used to check whether the residual of the model is a white noise sequence. The test results are shown in Table 2, which indicates that when the residual sequence was delayed 1-12 orders, the P value of Q statistics is greater than 0.05. Therefore, at the significance level of 0.05, the original hypothesis is not rejected, meaning that the residual sequence is a white noise sequence, indicating that the fitted model had fully extracted the information in the time series. For the residual distribution problem, we generated the model diagnosis report and analyzed the abnormal behavior of the research model, as shown in Figure 4. Figure 4a shows that the red KDE line follows the N (0, 1) line, which indicates that the residuals are normally distributed. Figure 4b shows that the residual error does not have autocorrelation, which indicates the model can help us understand the original time series data and predict the future values. Using the HJ-1 NBAR data and MODIS NBAR data from interest areas 1 and 2 in 2011-2013 as the raw data, the model was used to predict the reflectivity of the red and NIR bands in 2014, and the results were compared with the surface measured data to discuss the prediction accuracy of the model.