Structured low-rank matrix completion for forecasting in time series analysis
This work addresses forecasting challenges in time series analysis, but it appears incremental as it builds on existing low-rank matrix completion methods with specific adaptations.
The paper tackles the problem of forecasting in time series analysis using low-rank matrix completion for Hankel matrices with a nuclear norm convex relaxation, showing that the approach can work based on theoretical and numerical examples, with results emphasizing the importance of proper weighting for known observations.
In this paper we consider the low-rank matrix completion problem with 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 when the proposed approach can work. Our results highlight the importance of choosing a proper weighting scheme for the known observations.