Multivariate Extrapolation: A Tensor-Based Approach

Tensor extrapolation attempts to integrate temporal link prediction and time series analysis using multi-linear algebra. It proceeds as follows. Multi-way data are arranged in the form of tensors, i.e., 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 special cases and typical applications of link prediction. The paper at hand connects state-of-the-art tensor decompositions with a general class of state-space time series models. In doing so, it offers a useful framework to summarize existing literature and provide various extensions to it. Moreover, it overcomes the boundaries of classical link prediction and examines the application requirements in traditional fields of time series analysis. A numerical experiment demonstrates the superiority of the proposed method over univariate extrapolation approaches in terms of forecast accuracy.