Least squares parameter estimation for uncertain fractional differential equations and application to stock model

Abstract

In recent years, uncertain fractional differential equations was proposed for the description of complex uncertain dynamic systems with historical characteristics. For wider applications of uncertain fractional differential equations, researches on parameter estimation for uncertain fractional differential equations are of great importance. In this paper, based on the thought of least squares estimation and uncertain hypothesis test, an algorithm of parameter estimation for uncertain fractional differential equations is discussed. Finally, we consider the application of uncertain fractional differential equations based model to predict the forecasting stock price of three major indexes of U.S. stocks and make a comparison between uncertain fractional differential equations, uncertain differential equations and stochastic differential equations.