# Matrix factorization for multivariate time series analysis

## TL;DR

This paper investigates the statistical performance of matrix factorization in multivariate time series analysis, extending existing results to time-dependent data and showing improved convergence rates with structured series.

## Contribution

It extends matrix estimation theory from i.i.d. data to time series and demonstrates enhanced convergence rates for structured series like periodic or smooth ones.

## Key findings

- Extended matrix factorization results to time series data.
- Proved improved convergence rates for structured time series.
- Provided theoretical insights into statistical performance.

## Abstract

Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical performances of matrix factorization for time series. In this paper, we extend the results known for matrix estimation in the i.i.d setting to time series. Moreover, we prove that when the series exhibit some additional structure like periodicity or smoothness, it is possible to improve on the classical rates of convergence.