The positive promotion of regional economic growth is largely consistent with expectations, while there is also a promotion effect on the economic growth of neighboring regions. In this paper, the individual cognitive term of the particle swarm algorithm is introduced into the bath algorithm, and economic forecasting analysis is carried out based on the improved combination of grey model improvements. The main reason for the negative correlation between government investment and economic growth is that, although OFDI promotes economic growth, industrial upgrading, and optimizes industrial structure, it may also reduce regional export capacity, reduce employment opportunities, and increase agency costs. The estimated coefficients for human capital, labor input, capital stock, and urbanization rate are all positive, indicating that each variable is conducive to promoting regional economic growth.

To address the complexity of urban economic data and the problem that traditional forecasting methods do not fully utilize the correlation of data, resulting in low prediction accuracy, an urban economic forecasting model based on the fusion of deep belief neural (DBN) and long-short term memory (LSTM) is proposed. The model is based on a combination of DBN and LSTM. The model first uses bandpass filtering to denoise the urban economic data and then determines the prediction starting point of the model based on the root-mean-square and cliff features in the trend diagram of the urban economy; secondly, the optimised 4-layer DBN network is used for deep feature extraction and training and testing of the LSTM. The reliability of the proposed model is demonstrated through urban economic experiments, and the prediction results are compared with those of traditional LSTM, BP (back propagation) neural network, and DBN-BP model to verify the effectiveness of the model.