A Note on Physical Dependence and Mixing Conditions for Triangular Arrays

TL;DR

This paper establishes explicit bounds linking physical dependence measures to $eta$-mixing coefficients in triangular arrays, showing that weak physical dependence implies various mixing conditions, thus extending prior results.

Contribution

It provides explicit bounds connecting physical dependence and $eta$-mixing, demonstrating that weak physical dependence leads to mixing properties in triangular arrays, complementing previous work.

Findings

Explicit bounds on $eta$-mixing coefficients in terms of physical dependence.

Weak physical dependence implies $eta$-mixing and strong mixing.

Extends Hill (2025) by relaxing moment assumptions.

Abstract

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