Tensor extrapolation: Forecasting large-scale relational data

Tensor extrapolation attempts to forecast relational time series data using multi-linear algebra. It proceeds as follows. Multi-way data are arranged in the form of tensors, ie multi-dimensional arrays. Tensor decompositions are then used to retrieve periodic patterns in the data. Afterwards, these patterns serve as input for time series methods. However, previous approaches to tensor extrapolation are limited to preselected time series approaches and binary data. To permit automatic forecasting, the paper at hand connects state-of-the-art tensor decompositions with a general class of state-space time series models. Moreover, it highlights the need for data preprocessing in settings with real-valued data. In doing so, it enables data-driven model selection and estimation in large-scale forecasting problems. Numerical experiments show the effectiveness of the proposed method in identifying relevant underlying patterns and demonstrate its superiority over established extrapolation methods in terms of forecast accuracy.