Construction of Development Momentum Index of Financial Technology by Principal Component Analysis in the Era of Digital Economy

The purpose is to study applying mathematical analysis in financial technology (FinTech) development in the era of digital economy. An Evaluation Index System (EIS) for the current situation of Chinese FinTech enterprises is established by considering the impact of the era of the digital economy on the development of FinTech. Specifically, the Principal Component Analysis (PCA) is introduced to construct the principal component prediction model based on functional data. Then, six Chinese State-owned Enterprises (SOEs) are selected. Their stock prices are predicted using the proposed model through an empirical study. The results show that selecting three principal components to evaluate the financial situations of six SOEs is reasonable. The accumulated variance values of the first three principal components of the stock's closing price and opening price are all greater than 85%. Thus, the selected three principal components can obtain the potential information of the original data. The gap between the actual value and the proposed model-predicted value of the stocks of the six SOEs is relatively small. The Root Mean Square Error (RMSE) of China National Petroleum Corporation (CNPC) is 0.105, more than 10%. The predicted values of Huadian Energy and China Shenhua are 9.4% and 8.5%, respectively, second only to CNPC. Therefore, the proposed principal component prediction model based on functional data can predict the closing price of stocks well. The accuracy is relatively high and matches well with financial data analysis. This research has important implications for the development of FinTech.