ARMA, regular, and singular time series in 1D
Marianna Bolla, Tamás Szabados · 2021
In this chapter, the authors collect some basic facts about important classes of 1D (one-dimensional) stationary time series as a motivation for the multidimensional studies. They do it inductively, while proceeding from the simplest 1D processes to more and more general ones. In particular, in the chapter, the authors borrowed some ideas that they very much liked in Lamperti&s;s book. Under certain conditions, a TLF, applied to a white noise process, results in a sliding summation. The Wold decomposition in 1D guarantees that any non-singular weakly stationary time series can be decomposed into a regular and a singular process that are orthogonal to each other.