Beyond point forecasts: Uncertainty quantification in tensor extrapolation for relational time series data

Abstract

Contemporary data sets are frequently relational in nature. In retail, for example, data sets are more granular than traditional data, often indexing individual products, outlets, or even customers, rather than aggregating them at the group level. Tensor extrapolation aims to forecast relational time series data; it combines tensor decompositions and time series extrapolation. However, previous approaches to tensor extrapolation are restricted to point forecasts and fail to quantify the uncertainty associated with the forecasts. This paper provides prediction intervals within which we expect the true future values to lie with a specified probability. Numerical experiments suggest the effectiveness of the proposed method in terms of forecast performance. Moreover, the approach proves to be up to 77 times faster than the univariate competitor. For this reason, it exerts positive influence on both inclusiveness and the environment.