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

arXiv: https://arxiv.org/abs/2206.05103 · HTML: https://mlsanity.com/paper/2206.05103/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 123 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Robust Spectral Compressed Sensing via Structured Matrix Completion](https://mlsanity.com/paper/1304.8126/) (2013)
- [Top-N Recommender System via Matrix Completion](https://mlsanity.com/paper/1601.04800/) (2016)
- [A convex relaxation to compute the nearest structured rank deficient matrix](https://mlsanity.com/paper/1904.09661/) (2019)
- [Structured low-rank matrix completion for forecasting in time series analysis](https://mlsanity.com/paper/1802.08242/) (2018)
- [Low-rank Optimization with Convex Constraints](https://mlsanity.com/paper/1606.01793/) (2016)
- [A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery](https://mlsanity.com/paper/1609.07429/) (2016)
- [Variable projection methods for approximate (greatest) common divisor computations](https://mlsanity.com/paper/1304.6962/) (2013)
- [Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package](https://mlsanity.com/paper/1309.5050/) (2013)
- [Exact Solutions in Structured Low-Rank Approximation](https://mlsanity.com/paper/1311.2376/) (2013)
- [Robust Structured Low-Rank Approximation on the Grassmannian](https://mlsanity.com/paper/1506.03958/) (2015)
- [Iterative algorithms for weighted and unweighted finite-rank time-series approximations](https://mlsanity.com/paper/1507.02751/) (2015)
- [Denoising and Completion of Structured Low-Rank Matrices via Iteratively Reweighted Least Squares](https://mlsanity.com/paper/1811.07472/) (2018)
- [A hybrid penalty method for a class of optimization problems with multiple rank constraints](https://mlsanity.com/paper/1906.10396/) (2019)

## Built on by (most cited first, 1 of 1)

- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)

## Abstract (arXiv)

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.