Statistics and Its Interface

Volume 16 (2023)

Number 2

Special issue on recent developments in complex time series analysis – Part II

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

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

Pages: 287 – 303



Jonathan Gillard (School of Mathematics, Cardiff University, Cardiff, United Kingdom)

Konstantin Usevich (Université de Lorraine, CNRS, CRAN, Nancy, France)


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.


time series analysis, low-rank approximation, matrix completion, nuclear norm

2010 Mathematics Subject Classification

Primary 62M10, 62M15. Secondary 62P99.

Received 16 June 2021

Accepted 1 April 2022

Published 13 April 2023