## 3 Results
### Temporal Variation Characteristics of TCWV in China
#### 3.2.3 Prediction of TCWV in China Based on SARIMA  
The SARIMA model was used to predict the TCWV in China, and the monthly average value of TVWV from September 2002 to February 2022 was used as the original sample. The time series diagram and autocorrelation partial correlation diagram of TCWV are shown in Figure 7, and the lag of the autocorrelation coefficient in Figure 7 is set to 45. It can be seen from Figure 7 that the variation range of TCWV data is 10-35 kg/m\({}^{2}\). The Dickey-Fuller (DF) unit root test was performed on it, and a \(p\)-value = 0.39810 was obtained, meaning that the data accepted the null hypothesis, which implies that the data are non-stationary. Seasonal fluctuations in a time series can lead to the non-stationarity of a time series, which can be analyzed by constructing a SARIMA model. Therefore, seasonal difference and first-order difference were performed on the time series to make the data become stable. Figure 5: Monthly and seasonal variation of TCWV in China (2003–2021). (**a**) Monthly. (**b**) Seasonal. The seasonal difference of the original time series is shown in Figure 8. A simple subtraction operation is performed on the sequence, and the time difference is the seasonal cycle (here we set the seasonal cycle to 12, because a year is 12 months). It can be seen from Figure 8 that \(p=0.00002\), which is much less than 0.05; that is, the data is a stationary series, which means that the seasonality is eliminated. It can be seen from the autocorrelation partial correlation diagram in Figure 8 that the series still has significant time lags, so we continue to perform differential processing on the series. The first-order difference processing is performed on the time sequence, as shown in Figure 9, and the obtained \(p\)-value = 0, that is, the sequence is a stationary sequence. Then we perform a white noise test on it. This paper also uses the unit root test method, which in this particular case is the DF unit root test. The p-values obtained are far less than 0.01, 0.05, and the test is passed. That is, the obtained sequence is a stationary time series and a non-white noise sequence. By observing Figure 9, it can be preliminarily assumed that p = 3, because in the partial autocorrelation function (PACF) diagram, the maximum lag value that can be observed; since the first-order difference is made, assume that d = 1; because the 12 th-order lag is obvious in the autocr  
Figure 6: Mann-Kendall statistic curve of TCWV in seasonal in China. (**a**) Winter. (**b**) Spring. (**c**) Summer. (**d**) Autumn. Figure 7: Time series, autocorrelation and partial autocorrelation of TCWV. diagram, assume that Q = 1. Finally, the trial and error method is used near the initially determined parameters, and the final parameters are determined according to the principle of Akaike Information Criterion (AIC) minimum, and the final time series prediction model of monthly average TCWV in China is determined as SARIMA (3, 1, 3) \(\times\) (0, 1, 1, 12). The residual test was carried out on the stablished SARIMA model, and the autocorrelation graph test was used in this paper. As shown in Figure 10, except when lag = 0 oversteps 95% confidence interval, the rest are in the confidence interval. This shows that the fitting effect of the model is relatively good, and the original time series data can be understood and the future numerical value can be predicted. The timing diagram of the finally drawn prediction sequence is shown in Figure 11. The abscissa represents the month, and the ordinate represents the values of TCW. The blue curve is the true value, the red curve is the predicted value, and the red curve of the shadow part is the monthly average trend of TCWV in the next full year. It can be seen from Figure 11 that the predicted values are in good agreement with the actual ones. Furthermore, the mean absolute percentage error (MAPE), mean square error (MSE) and R\({}^{2}\)-score were calculated to judge the SARIMA model. The MAPE is 2.65%, MSE is 0.329 and R\({}^{2}\)-score is 0.9949.