A Note on Physical Dependence and Mixing Conditions for Triangular Arrays

arXiv (Cornell University)

Abstract

Under mild structural assumptions and regularity conditions on the marginal and conditional densities, an explicit bound on the $β$-mixing coefficients in terms of the physical dependence measure is provided. Consequently, weak physical dependence implies $β$-mixing and strong mixing for triangular arrays, complementing Hill (2025), who proved the converse implication under moment assumptions.

Authors 1

1. Florian Heinrichs corresponding Aachen Department of Medical Engineering and Technomathematics

   FH Aachen

   Affiliation as printed

   Department of Medical Engineering and Technomathematics , FH Aachen -University of Applied Sciences , Heinrich-Mußmann-Straße 1 , Jülich , 52428 , Germany