Modeling Hierarchical Seasonality Through Low-Rank Tensor Decompositions in Time Series Analysis

Abstract

Accurately representing periodic behavior is a frequently encountered challenge in modeling time series. This is especially true for observations where multiple, nested seasonalities are present, which is often encountered in data that pertain to collective human activity. In this work, we propose a new method that models seasonality through the multilinear representations that characterize low-rank tensor decompositions. We show that the tensor formalism accurately describes multiple nested periodic patterns, and well-known tensor decompositions can be used to parametrize cyclical patterns, leading to superior generalization and parameter efficiency. Furthermore, we develop a Bayesian variant of our approach which facilitates extraction of these seasonal patterns in an interpretable fashion from large-scale datasets, providing insight into the underlying dynamics that create such emergent behavior. We lastly test our method in missing data imputation, where the results show that our method couples interpretability with accuracy in time series analysis.

Keywords

• Time series analysis
• nonnegative tensor factorization
• seasonality
• tensor decomposition
• Bayesian model selection