Regular multidimensional stationary time series

TL;DR

This paper provides a simplified sufficient condition for regularity in high-dimensional stationary time series and demonstrates how such processes can be approximated by lower-rank regular processes, which are crucial in high-dimensional data analysis.

Contribution

It introduces a more accessible condition for regularity and shows how regular processes can be approximated by lower-rank processes, enhancing analysis of high-dimensional data.

Findings

Simpler sufficient condition for regularity in weakly stationary time series.

Regular processes can be approximated by lower-rank regular processes.

Highlights importance of regular processes in high-dimensional data analysis.

Abstract

The aim of this paper is to give a simpler, more usable sufficient condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how regular processes satisfying these sufficient conditions can be approximated by a lower rank \emph{regular} process. The relevance of these issues is shown by the ever increasing presence of high-dimensional data in many fields lately, and because of this, low rank processes and low rank approximations are becoming more important. Moreover, regular processes are the ones which are completely influenced by random innovations, so they are primary targets both in the theory and applications.