Statistical Inference of Uncertain Autoregressive Model via the Principle of Least Squares

Abstract

In the study of uncertain autoregressive models, how to estimate the unknown parameters and uncertain disturbance term in the models is always a key problem. In view of this, this paper proposes a statistical inference method based on the principle of least squares to determine the unknown parameters and uncertain disturbance term in an uncertain autoregressive model, and designs a numerical algorithm to calculate the numerical solutions of the corresponding estimators. Then, the uncertain hypothesis test is used to verify the applicability of the estimated uncertain autoregressive model, and point forecast and interval forecast are also made for the time series of future moments. Finally, a case study of the Consumer Price Index for all items in U.S. cities is provided to illustrate the effectiveness of the approach proposed in this paper.