Mathematical Modelling of Gross Domestic Product Prediction in United States Based on Logistic Map

Abstract

Gross domestic product (GDP) measures a country's economic development. However, uncertain factors affecting the growth of a GDP cause the GDP prediction to be difficult and inaccurate. This research describes the GDP prediction of the United States through the mathematical modelling of a logistic map model. The GDP historical data from 1960 to 2023 are collected and visualized for prediction purposes. A least square optimization problem is introduced, where the objective function is to minimize the sum of square errors for the differences between the model and the actual GDP data. The gradient method is applied to solve the least squares optimization problem and, in turn, to estimate the model parameters optimally and to update the model solution iteratively until convergence. The predictive solution of the GDP is obtained with these optimal parameters. From the simulation results, an initial solution with a sigmoid curve gives a more accurate prediction solution that is closely aligned with the actual GDP data. The parameters in the logistic map model have been successfully estimated, and the predicted GDP results in the United States give a small mean square error value. In conclusion, the logistic map model is efficient for predicting the United States' GDP.