  This work proposes a novel approach for multiple time series forecasting. At
first, multi-way delay embedding transform (MDT) is employed to represent time
series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors
are projected to compressed core tensors by applying Tucker decomposition. At
the same time, the generalized tensor Autoregressive Integrated Moving Average
(ARIMA) is explicitly used on consecutive core tensors to predict future
samples. In this manner, the proposed approach tactically incorporates the
unique advantages of MDT tensorization (to exploit mutual correlations) and
tensor ARIMA coupled with low-rank Tucker decomposition into a unified
framework. This framework exploits the low-rank structure of block Hankel
tensors in the embedded space and captures the intrinsic correlations among
multiple TS, which thus can improve the forecasting results, especially for
multiple short time series. Experiments conducted on three public datasets and
two industrial datasets verify that the proposed BHT-ARIMA effectively improves
forecasting accuracy and reduces computational cost compared with the
state-of-the-art methods.
