## 3 Results
### Topic Dynamics  
#### 3.3.1 Prediction Based on Autoregressive Integrated Moving Average Technology (ARIMA)  
Because the article count sequence shows strong autocorrelation, we chose autoregressive integrated moving average technology (ARIMA) to determine trends across the entire field and each topic. In ARIMA (\(p,d,q\)), the AR part can be regarded as the linear regression of the previous \(p\) period time series; the MA part is regarded as the linear regression of the current time series with respect to the random disturbance of the previous \(q\) period; and the \(d\) part represents \"difference\", that is, in order to obtain data on the stationary series, the non-stationary data values are replaced by the difference between their values and one or more previous values. In this study, 30-time series were constructed based on ARIMA, and the appropriate parameters of ARIMA were determined following the conventional Baux Jenkins methodology [15]. Taking the whole field as an example, first, the text was divided into a training set (90%) and a test set (10%). We used the data from 1992 to 2015 as a training set and the data from 2015 to 2018 as a test set. Then, the time sequence diagram (part of the curve in Figure 1) of the percentage of publications in this field (1992-2018) was drawn. We found that it has a strong growth trend and poor stability. Because the ARIMA model requires the time series to be stable, this study took the logarithm and first-order difference to obtain the stable series. At the same time, the results of the Dickey fuller test of the first-order difference sequence also meet the requirements of stationarity. Then, the AR order of the training sequence was estimated by the partial autocorrelation function (PACF) graph; the MA order of the training sequence was estimated by the autocorrelation function (ACF) graph; and the most appropriate \(p\), \(q\) combination value was selected by combining the Akaike information (AIC), Bayesian information (BIC), and Hannan and Quinn information standard (HQIC). For the time series of the whole field, when \((p,q)=(3,2)\), the standard statistics of AIC, BIC, and HQIC are the smallest, and are \(-298.89\), \(-292.42\), and \(-296.97\), respectively. In order to verify the quality of the model, we drew the residual to see whether it was white noise, and checked whether the residual was non autocorrelation by applying the Durbin Watson test and Ljung box test [16]. The Durbin Watson test value was \(1.71\), close to \(2\), indicating that there was no autocorrelation. Finally, through the comparison of the prediction results and the test set, it was found that the results were relatively similar, indicating that the prediction model fitted well. As shown in Figure 1, this study placed the predicted results on the same map as the historical data. In addition, as shown in Table 5, this research found the ARIMA model parameters \((p,d,q)\) for each topic and calculated the annual average of the predicted growth rate. We analyzed the overall growth in this field, which experienced a volatility increase before 2005 and began to grow steadily after 2005. We discussed the dynamics of each topic in the 1992-2005 and 2005-2018 time periods. We constructed 30 time series (the field and 29 topics). The percentage of publications in this field has increased significantly in both time periods, with an average growth rate of 23.98% before 2005 and 25.49% after 2005. However, there were only eight topics before 2005, and six of them had a decline in the growth rate before 2005, but then exhibited an increase after 2005. For example, the publication percentage of \"Energy storage or reserve system\" (Topic 6) shrank (on average, \(-0.31\%\) per year) before 2005, but expanded (on average, \(111.0\%\) per year) in the second period. \"Prediction and management of renewable resources\" (Topic 20) declined by an average of 33.6% per year before 2005, but increased by an average of 46.0% per year during the second period.