Maximum likelihood estimation for uncertain autoregressive moving average model with application in financial market

Abstract

Uncertain time series analysis is an influential component of statistics that employs chronological data for further application in forecasting and control. As basic time series models, the uncertain autoregressive model and uncertain moving average model can not deal with the situation where the current observation is impacted by both the past observations and the past disturbance terms. This motivates us to initiate an uncertain autoregressive moving average model for obtaining better flexibility and general ability in actual problems. First, this paper presents a maximum likelihood estimation for calculating the parameters of the uncertain autoregressive moving average model and defines a mean absolute deviation criterion to identify it. This procedure is applied to the range return of the financial market, which is obtained from low and high prices of the corresponding trading day. Then, two examples of gold futures price and Microsoft stock price are applied to illustrate the accuracy of this method. The uncertain hypothesis test is used to analyze the properties of the residuals and correct for outliers. Finally, two comparative analyses are given to show the robustness of maximum likelihood estimation in the presence of outliers and the need to introduce the uncertain autoregressive moving average model.