Analytic solution of uncertain autoregressive model based on principle of least squares

Abstract

Uncertain time series is a method to predict future values based on previously uncertain observed values, which is firstly proposed by Yang and Liu (Fuzzy Optim Decis Mak, 2019. https://doi.org/10.1007/s10700-018-9298-z). This paper continues to study a special uncertain time series—uncertain autoregressive model, and gives an analytic solution of uncertain autoregressive model based on the principle of least squares. Moreover, this paper proves another equivalent form to calculate the unknown parameters of uncertain autoregressive model via uncertainty distribution and also analyzes the disturbance term via uncertainty distribution.