Abstract: To solve the prediction problem of high-dimensional time series with missing values， a tensor autoregressive completion algorithm is proposed. Based on the high-precision low-rank tensor completion algorithm （HaLRTC）， the tensor autoregressive norm is added， and the missing data of the tensor time series is completed by making full use of the information of all dimensions 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 autoregressive tensor completion （CCAR）， the core tensor autoregressive completion （CTAR）， and the tensor core autoregressive completion （TCAR） based on Tucker decomposition are proposed for ablation experiment. The results of ablation experiments and comparison experiments with other existing methods show that the proposed algorithm has obvious prediction advantages in the case of small proportion of missing data.

Key words:  , time series forecasting； tensor decomposition； tensor completion； nuclear norm； autoregressive model