Abstract

Uncertain time series analysis is a methodology that deals with expert’s experimental time series data. Previous studies mainly focus on linear models such as an uncertain autoregressive (UAR) model. Nevertheless, the laws of motion in the real world are usually non linear. In order to model the observations that periodically vary over time, this article introduces an uncertain threshold autoregressive (UTAR) model. Then unknown parameters in the UTAR model can be estimated with the least squares estimation and residual analysis is presented. Furthermore, we discuss the forecast value and confidence interval for variables in the next periods. Ultimately, a numerical example is given.

摘要

不确定时间序列分析是一种处理专家实验时间序列数据的方法。以前的研究主要集中在线性模型，例如不确定的自回归（UAR）模型。然而，现实世界中的运动定律通常是非线性的。为了对随时间周期性变化的观测值进行建模，本文引入了一个不确定阈值自回归 (UTAR) 模型。然后可以用最小二乘估计估计UTAR模型中的未知参数，并提出残差分析。此外，我们讨论了未来时期变量的预测值和置信区间。最后给出一个数值例子。