Abstract

Uncertain time series models have been investigated to predict future values based on imprecise observations. The existing researches focus on how to estimate unknown parameters in the uncertain time series model without considering how to determine the lag order. This paper proposes three types of cross validation methods, i.e. fixed origin cross validation, rolling origin cross validation, and rolling window cross validation to choose the lag order considering the model’s prediction ability, and derives corresponding calculation methods under the framework of uncertainty theory. A numerical example and a real data example illustrate our methods in detail.

摘要

已经研究了不确定的时间序列模型，以根据不精确的观察预测未来值。现有的研究主要集中在如何估计不确定时间序列模型中的未知参数，而没有考虑如何确定滞后阶。本文提出了三种交叉验证方法，即固定原点交叉验证、滚动原点交叉验证和滚动窗口交叉验证来选择考虑模型预测能力的滞后阶数，并在不确定性理论框架下推导出相应的计算方法。一个数值示例和一个真实数据示例详细说明了我们的方法。