Basic Properties of Strong Mixing Conditions.

Archimedean Copulas and Temporal Dependence

“…Theorem 21.19 in Bradley (2007). The β-mixing coefficients for {U t } are bounded from below by the corresponding α-mixing coefficients.…”

“…In contrast, the Archimedean copula in Example 4.1 is absolutely continuous with respect to Lebesgue measure on the unit square, and admits a density that is positive almost everywhere. Using, for instance, Theorems 21.3 and 21.5 in Bradley (2007), one may show that this property implies that {U t } is ergodic and β-mixing. The rates of ergodicity and β-mixing are, however, subexponential.…”

Nonlinear system theory: Another look at dependence

“…Since then, as basic assumptions on the dependence structures, the strong mixing condition and its variants have been widely used and various limit theorems have been obtained; see the extensive treatment in ref. 6. Since the quantity ͉‫(ސ‬A പ B) Ϫ ‫(ސ‬A)‫(ސ‬B)͉ in Eq.…”

Sequential monitoring of the tail behavior of dependent data

“…, X m ). For more on this mixing concept we refer to Bradley (2007). In order to construct a monitoring procedure for a tail index change, we have to assume tail index (or, equivalently, extreme value index) constancy over some historical period (also called training period) of suitable length n:…”