Structured low-rank matrix completion for forecasting in time series analysis

Jonathan Gillard (1) , Konstantin Usevich (2)

1 School of Mathematics [Cardiff]
2 CRAN - Centre de Recherche en Automatique de Nancy

This paper considers the low-rank matrix completion problem, with a specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices and a convex relaxation based on the nuclear norm. Based on new theoretical results and a number of numerical and real examples, we investigate the cases in which the proposed approach can work. Our results highlight the importance of choosing a proper weighting scheme for the known observations.

Mots clés: Nuclear norm; Forecasting; Low-rank matrix completion; Hankel matrices

Domaines: Méthodologie [stat.ME]

Jonathan Gillard, Konstantin Usevich. Structured low-rank matrix completion for forecasting in time series analysis. International Journal of Forecasting, 2018, 34 (4), pp.582-597. ⟨10.1016/j.ijforecast.2018.03.008⟩. ⟨hal-01983158⟩