Manfred Deistler and the General-Dynamic-Factor-Model Approach to the Statistical Analysis of High-Dimensional Time Series

Abstract

For more than half a century, Manfred Deistler has been contributing to the construction of the rigorous theoretical foundations of the statistical analysis of time series and more general stochastic processes. Half a century of unremitting activity is not easily summarized in a few pages. In this short note, we chose to concentrate on a relatively little-known aspect of Manfred’s contribution that nevertheless had quite an impact on the development of one of the most powerful tools of contemporary time series and econometrics: dynamic factor models.

Inferential theory for generalized dynamic factor models

“…In both cases, the model is considered as the description of a very specific data-generating process (no representation result), hence requires being checked; all the component functional time series, moreover, have to take values in the same Hilbert space, which is somewhat restrictive. Hallin et al (2023); Tavakoli et al (2023), on the other hand, extend to the functional case the approximate static model of Chamberlain, and establish a representation result; the component time series may take values in different Hilbert spaces, including the real line.…”