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

TL;DR

This paper introduces a low-rank matrix completion approach using nuclear norm relaxation for time series forecasting, emphasizing the importance of proper weighting schemes for accurate imputation.

Contribution

It provides new theoretical insights and practical guidelines for applying low-rank matrix completion to time series forecasting, especially with Hankel matrices.

Findings

Proper weighting schemes improve imputation accuracy

The approach works well on numerical and real data

Theoretical results support practical effectiveness

Abstract

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.