Tight Risk Bound for High Dimensional Time Series Completion

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

1 RIKEN AIP - RIKEN Center for Advanced Intelligence Project [Tokyo]
2 MODAL'X - Modélisation aléatoire de Paris X
3 ESME - ESME - École spéciale de mécanique et d'électricité

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the application of these methods to dependent datas. In this paper, we propose a general model for multivariate, partially observed time series. We show that the least-square method with a rank penalty leads to reconstruction error of the same order as for independent datas. Moreover, when the time series has some additional properties such as periodicity or smoothness, the rate can actually be faster than in the independent case.

Domaines: Statistiques [math.ST]

Pierre Alquier, Nicolas Marie, Amélie Rosier. Tight Risk Bound for High Dimensional Time Series Completion. Electronic Journal of Statistics , 2022, 16 (1), pp.3001-3035. ⟨10.1214/22-EJS2015⟩. ⟨hal-03142254v3⟩