Consistency of Generalized Dynamic Principal Components in Dynamic Factor Models

TL;DR

This paper proves that generalized dynamic principal components reliably reconstruct the common factors in dynamic factor models as data size grows, supported by simulation results.

Contribution

It establishes the theoretical consistency of generalized dynamic principal components in dynamic factor models, extending previous work.

Findings

Reconstruction converges in mean square to the common part as data size increases.

Simulation results support the theoretical convergence.

Provides a rigorous foundation for using generalized dynamic principal components in large datasets.

Abstract

We study the theoretical properties of the generalized dynamic principal components introduced in Pe\~na and Yohai (2016). In particular, we prove that when the data follows a dynamic factor model, the reconstruction provided by the procedure converges in mean square to the common part of the model as the number of series and periods diverge to infinity. The results of a simulation study support our findings.