用于具有缺失值的时间序列预测的张量自回归补全算法

Prediction of Time Series with Missing Value Based on Tensor Autoregressive Completion

为解决具有缺失值的高维时间序列的预测问题,提出一种张量自回归补全算法。在高精度低秩张量补全算法(HaLRTC)的基础上,加入张量自回归范数,通过充分利用高维时间序列所有维度的信息,对张量时间序列缺失数据进行补全。其中张量核范数捕捉时间序列的长期趋势,张量自回归范数捕捉时间序列的短期趋势,利用自回归模型的高阶形式,对补全后的高维时间序列进行预测。为了验证算法的有效性,提出基于Tucker分解的核心自回归张量补全算法(CCAR)、核心张量自回归补全算法(CTAR)、张量核心自回归补全算法(TCAR)用于消融实验。通过消融实验以及与其他现有方法的对比实验结果表明,在数据缺失比例较小的情况下,本文所提出的算法具有明显的预测优势。

To solve the prediction problem of high-dimensional time series with missing values,a tensor autoregressive comple⁃tion algorithm is proposed.Based on the high-precision low-rank tensor completion algorithm(HaLRTC),the tensor autoregres⁃sive norm is added,and the missing data of the tensor time series is completed by making full use of the information of all dimen⁃sions of the high-dimensional time series,in which the tensor kernel norm captures the long-term trend of the time series,and the tensor autoregressive norm captures the short-term trend of the time series.Using high-order form of the autoregressive model,the completed high-dimensional time series is predicted.To verify the effectiveness of the algorithm,the core autoregres⁃sive tensor completion(CCAR),the core tensor autoregressive completion(CTAR),and the tensor core autoregressive comple⁃tion(TCAR)based on Tucker decomposition are proposed for ablation experiment.The results of ablation experiments and com⁃parison experiments with other existing methods show that the proposed algorithm has obvious prediction advantages in the case of small proportion of missing data.