Parameter Estimation in Multifactor Uncertain Differential Equation with Symmetry Analysis for Stock Prediction

Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasingly important. Thus, how to estimate unknown parameters in a MUDE under a multi-source noise environment is a challenge. To address this, this paper innovatively proposes a moment method to estimate the unknown parameters in a MUDE and illustrates two numerical examples to show the process of estimating parameters. Furthermore, since the system or environment is complex and constantly changing, the parameters in the MUDE are not constants but time-varying functions in many cases. Therefore, parameter estimation for time-varying functions is another challenge. In order to deal with this, this paper develops a method of parameter estimation for time-varying functions in the MUDE based on the moment method. As an application, this method of parameter estimation for time-varying functions is used to model China Merchants Bank stock.