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.
翻译:本文的目的是为一般的薄弱固定时间序列的常规性提供一个更简单、更实用的充足条件。 此外,这一条件还用来表明如何通过较低级别的 \ emph{ rogular} 进程来比较满足这些足够条件的常规程序。这些问题的相关性表现在最近许多领域高维数据日益增多,而且由于这种情况,低级程序和低级近似越来越重要。此外,常规程序是完全受随机创新影响的程序,因此在理论和应用方面都是主要目标。