Analysis of EUR to USD Exchange Rates with Uncertain Time Series Model and Uncertain Differential Equation

Abstract As a crucial theory and method to analyze and interpret data in practice by means of uncertainty theory, uncertain statistics is composed of some mathematical tools, and the two most important tools are uncertain time series analysis and uncertain differential equation. For the sake of predicting the future EUR to USD exchange rates, this paper uses the tools of uncertain time series analysis and uncertain differential equation to model the EUR to USD exchange rates from January 2018 to May 2023. Following that, the fitness of the estimated uncertain statistical models to the data set is also verified by using the uncertain hypothesis test. Finally, by means of testing the stochastic hypothesis of the estimated statistical model based on the specific residuals of the EUR to USD exchange rates, the inappropriateness of the stochastic statistical model is also pointed out in this paper.