Uncertain vector autoregressive smoothly moving average model

Abstract

Uncertain time series analysis is an effective method to predict the variable with time index under imprecise observations. Sometimes, the time series model is built directly on the data which the prediction result is inaccurate. In this paper, an uncertain vector autoregressive smoothly moving average model (UVARSMA) is given. The least absolute deviation estimation and the least square estimation are given to estimate the unknown parameters. In order to predict effectively, we analyze the residuals and give the point estimation and interval estimation about the prediction. The relevant results are compared with those of the uncertain vector autoregressive model. Finally, a practical example about air index in Beijing, from 9 March 2022 to 23 April 2022, is given to verify the feasibility and accuracy of the new model.