Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review

TL;DR

This paper reviews Hankel low-rank approximation and completion techniques, highlighting their applications in time series analysis and forecasting, discussing problem formulations, challenges, key theorems, and providing illustrative examples.

Contribution

It offers a comprehensive overview of Hankel low-rank methods in time series, including formulations, theoretical insights, and practical examples, summarizing current research and challenges.

Findings

Hankel low-rank methods are effective for time series completion and forecasting.

Global optimality in Hankel low-rank approximation remains challenging.

The paper provides key theorems and illustrative examples for understanding these methods.

Abstract

In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting. We begin by describing possible formulations of the problem and offer commentary on related topics and challenges in obtaining globally optimal solutions. Key theorems are provided, and the paper closes with some expository examples.