A Note on Physical Dependence and Mixing Conditions for Triangular Arrays

Abstract

Under mild structural assumptions and regularity conditions on the marginal and conditional densities, an explicit bound on the ${\hat{I}}^2$-mixing coefficients in terms of the physical dependence measure is provided. Consequently, weak physical dependence implies ${\hat{I}}^2$-mixing and strong mixing for triangular arrays, complementing Hill (2025), who proved the converse implication under moment assumptions.

Keywords: Weak Dependence, Strong Mixing, ${\hat{I}}^2$-Mixing, Physical Dependence, Triangular Arrays, Local Stationarity