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Time-series prediction has become a prominent challenge, especially when the data are described as sequences of multiway arrays. Because noise and redundancy may exist in the tensor representation of a time series, we focus on solving the problem of high-order time-series prediction under a tensor decomposition framework and develop two novel multilinear models: 1) the multilinear orthogonal autoregressive (MOAR) model and 2) the multilinear constrained autoregressive (MCAR) model. The MOAR model is designed to preserve as much information as possible from the original tensorial data under orthogonal constraints. The MCAR model is an enhanced version that is developed by replacing orthogonal constraints with an inverse decomposition error term. For both models, we project the original tensor into subspaces spanned by basis matrices to facilitate the discovery of the intrinsic temporal structure embedded in the original tensor. To build connections among consecutive slices of the tensor, we generalize a traditional autoregressive model to tensor form to better preserve the temporal smoothness. Experiments conducted on four publicly available datasets demonstrate that our proposed methods converge within a small number of iterations during the training stage and achieve promising results compared with state-of-the-art methods.

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