Least-squares estimation for uncertain moving average model

Abstract

An uncertain time series (UTS) is a sequence of uncertain observed values taken sequentially in time. As a basic UTS model, an uncertain autoregressive (UAR) model has been investigated. This paper proposes another fundamental model—uncertain moving average (UMA) model, whose uncertain observed value depends linearly on the current and various past values of an uncertain disturbance term. By converting the 1-order UMA model into a UAR model, parameters estimation is presented based on the least-squares method, and a minimization problem is derived to calculate the unknown parameters in the 1-order UMA model. Moreover, an approach is explored to estimate the expected value and variance of uncertain disturbance terms, and forecast value and confidence interval are also considered to predict the next value.

Keywords:

• Uncertain variable
• moving average
• uncertain disturbance
• forecast value
• confidence interval

Additional information

Funding

The authors gratefully acknowledge the financial support provided by National Natural Science Foundation of China (No. 71471038), Program for Young Excellent Talents in UIBE (No. 18YQ06), and the Fundamental Research Funds for the Central Universities in UIBE (No. CXTD10-05).