Matrix Factorization for Multivariate Time Series Analysis

Pierre Alquier (1) , Nicolas Marie (2, 3)

1 CREST - Centre de Recherche en Économie et Statistique
2 MODAL'X - Modélisation aléatoire de Paris X
3 ESME - ESME - École spéciale de mécanique et d'électricité

Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical performances of matrix factorization for time series. In this paper, we extend the results known for matrix estimation in the i.i.d setting to time series. Moreover, we prove that when the series exhibit some additional structure like periodicity or smoothness, it is possible to improve on the classical rates of convergence.

Mots clés: Random matrices; Multivariate time series analysis; Nonparametric regression; Matrix factorization

Domaines: Théorie [stat.TH]

Pierre Alquier, Nicolas Marie. Matrix Factorization for Multivariate Time Series Analysis. Electronic Journal of Statistics , 2019, 13 (2), pp.4346-4366. ⟨10.1214/19-EJS1630⟩. ⟨hal-02068455v2⟩