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edit approved May 30, 2014 at 15:46
Davide Giraudo
edit approved May 30, 2014 at 15:46
Davide Giraudo
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edited for LATEX, removed boilerplate, tweaked block quote
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edit approved Mar 10, 2014 at 19:09
Sycorax ♦
edit approved Mar 10, 2014 at 19:09
Sycorax ♦
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What are ρ$\rho$-, β$\beta$-, and α$\alpha$-mixing conditions?

I have seen properties named ρ$\rho$-, β$\beta$-, and α$\alpha$-mixing conditions in papers related to Copulas and Markov processes like this one:

In this paper, we identify conditions on C$C$ that suffice for geometrically geometrically fast mixing rates. Geometric β$\beta$-mixing, equivalent to geometric geometric ergodicity for sta- tionarystationary Markov chains, is established under under a rather strong condition that ex- cludesexcludes copulas that exhibit tail tail dependence or asymmetry.Geometric ρ Geometric $\rho$-mixing, which implies geometric α geometric $\alpha$-mixing, is obtained under a much weaker condition. We verify verify this condition for various parametric copula functions that are pop- ular popular in applied work. ρ$\rho$-, β$\beta$-, and α$\alpha$-mixing conditions may be used as as the basis for a range of inequalities and limit theorems that are useful useful in demonstrating the asymptotic validity of statistical methods; methods;

Beare, B., 2010, Copulas and temporal dependence, Econometrica, 78(1).

I am an engineering student and I have trouble understanding these conditions in statistical texts. Can somebody explain them? Thanks

What are ρ-, β-, and α-mixing conditions?

I have seen properties named ρ-, β-, and α-mixing conditions in papers related to Copulas and Markov processes like this one:

In this paper, we identify conditions on C that suffice for geometrically fast mixing rates. Geometric β-mixing, equivalent to geometric ergodicity for sta- tionary Markov chains, is established under a rather strong condition that ex- cludes copulas that exhibit tail dependence or asymmetry.Geometric ρ-mixing, which implies geometric α-mixing, is obtained under a much weaker condition. We verify this condition for various parametric copula functions that are pop- ular in applied work. ρ-, β-, and α-mixing conditions may be used as the basis for a range of inequalities and limit theorems that are useful in demonstrating the asymptotic validity of statistical methods;

Beare, B., 2010, Copulas and temporal dependence, Econometrica, 78(1).

I am an engineering student and I have trouble understanding these conditions in statistical texts. Can somebody explain them? Thanks

What are $\rho$-, $\beta$-, and $\alpha$-mixing conditions?

I have seen properties named $\rho$-, $\beta$-, and $\alpha$-mixing conditions in papers related to Copulas and Markov processes like this one:

In this paper, we identify conditions on $C$ that suffice for geometrically fast mixing rates. Geometric $\beta$-mixing, equivalent to geometric ergodicity for stationary Markov chains, is established under a rather strong condition that excludes copulas that exhibit tail dependence or asymmetry. Geometric $\rho$-mixing, which implies geometric $\alpha$-mixing, is obtained under a much weaker condition. We verify this condition for various parametric copula functions that are popular in applied work. $\rho$-, $\beta$-, and $\alpha$-mixing conditions may be used as the basis for a range of inequalities and limit theorems that are useful in demonstrating the asymptotic validity of statistical methods;

Beare, B., 2010, Copulas and temporal dependence, Econometrica, 78(1).

I am an engineering student and I have trouble understanding these conditions in statistical texts. Can somebody explain them?

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Fred
Fred
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What are ρ-, β-, and α-mixing conditions?

I have seen properties named ρ-, β-, and α-mixing conditions in papers related to Copulas and Markov processes like this one:

In this paper, we identify conditions on C that suffice for geometrically fast mixing rates. Geometric β-mixing, equivalent to geometric ergodicity for sta- tionary Markov chains, is established under a rather strong condition that ex- cludes copulas that exhibit tail dependence or asymmetry.Geometric ρ-mixing, which implies geometric α-mixing, is obtained under a much weaker condition. We verify this condition for various parametric copula functions that are pop- ular in applied work. ρ-, β-, and α-mixing conditions may be used as the basis for a range of inequalities and limit theorems that are useful in demonstrating the asymptotic validity of statistical methods;

Beare, B., 2010, Copulas and temporal dependence, Econometrica, 78(1).

I am an engineering student and I have trouble understanding these conditions in statistical texts. Can somebody explain them? Thanks