Parameter Estimation of Differential Equation Model based on Optimal Weight Choice Method

Abstract

Differential equations are important tools to portray dynamic problems, and are widely used in finance, engineering and biology. Here, multiple dynamic differential models were built innovatively, and discretized with the Runge-Kutta method. The the model parameters were estimated. The models were averaged using the Optimal weight selection method, and the consistency of such parameter estimation was verified. Numerical simulations were also conducted, and the simulated results outperformed ordinary linear models. Finally, the differential averaging model built here was used to empirically analyze the Shanghai Index 300. This method integrated the fluctuation features of multiple Shanghai Composite Index fitting models, and yielded good analytical results. This study provides a methodological reference for analysis of stock market situations, and offers research clues for the parameter estimation of differential equations.