A comprehensive analysis of digital inclusive finance's influence on high quality enterprise development through fixed effects and deep learning frameworks.

In the context of global economic transformation, high-quality enterprise development (HQED) is crucial for driving economic growth, particularly through enhancing Total Factor Productivity (TFPLP). Digital Inclusive Finance (DIF), as a classical financial model, plays an important role in promoting high-quality enterprise development. To explore the relationship between TFP and DIF, we first applied traditional double fixed-effects models, along with robustness and heterogeneity tests, for modeling experiments. This series of tests effectively revealed the theoretical linear relationships between economic variables. However, the double fixed-effects model has limitations in capturing nonlinear relationships and making predictions. Given the growing body of research on existing hybrid models, we acknowledge the importance of exploring and contributing to this evolving area. To address this issue, based on the results of traditional economic analysis, we introduced improved time series models. These advanced deep learning models allow us to better capture the complex nonlinear relationship between DIF and TFP. The experiment initially explored the preliminary structural relationship between DIF and TFP using double fixed-effects models combined with robustness and heterogeneity tests. Then, based on the results of these tests, we selected deep learning features and combined Kolmogorov-Arnold Neural Network (KAN), Graph Neural Network (GNN) models with classic time series deep learning models (Transformer, LSTM, BiLSTM, GRU) to capture the latent nonlinear features in the data for prediction. The results show that, compared to traditional time series forecasting methods, the improved deep learning models perform better in capturing the nonlinear relationships of economic variables, improving prediction accuracy, and reducing prediction errors. Finally, paired t-tests and Cohen's d effect size tests were used to evaluate error metrics, and the results indicate that the introduction of KAN and GNN models significantly improved the performance of time series forecasting models.