Pair-copula constructions of multiple dependence
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Citations
Risk Factors, Copula Dependence and Risk Sensitivity of a Large Portfolio
Using Copula distributions to support more accurate imaging-based diagnostic classifiers for neuropsychiatric disorders.
Copula-based synthetic data augmentation for machine-learning emulators.
Efficient Bayesian inference for nonlinear state space models with univariate autoregressive state equation
Bayesian Inference for Regression Copulas
References
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
Generalized autoregressive conditional heteroskedasticity
Remarks on Some Nonparametric Estimates of a Density Function
Related Papers (5)
Frequently Asked Questions (12)
Q2. What are the future works in "Pair-copula constructions of multiple dependence" ?
Further research is needed to produce better comparison methods between alternative pair-copulae and between alternative decompositions.
Q3. What is the h-function for sampling from a canonical vine?
Since all decompositions in the 3-dimensional case are both a canonical vine and a D-vine, the resulting sample will also be a sample from a D-vine.
Q4. What is the likelihood of the Student’s t-copula?
For Archimedean copulae, K(z) is given by an explicit expression, while for the Student’s t-copula is has to be numerically derived.
Q5. What is the way to test the dependency structure of a data set?
To verify whether the dependency structure of a data set is appropriately modelled by a chosen pair-copula decomposition, the authors need a goodness-of-fit (GOF) test.
Q6. What is the density of a canonical vine?
The n-dimensional density corresponding to a canonical vine is given byn ∏k=1f(xk) n−1 ∏j=1n−j ∏i=1cj,j+i|1,...,j−1 (F (xj |x1, . . . , xj−1), F (xj+i|x1, . . . , xj−1)) .
Q7. What is the probability of the pair-copula density for the pair S, T?
In Figure 8, the authors show the log-likelihood of the pair-copula density for the pair S, T as a function of νST , for ρST fixed to -0.21.
Q8. What is the function h(x, v,) used in Sections 4?
In Sections 4-7 the authors will use the function h(x, v,Θ) to represent this conditional distribution function when x and v are uniform, i.e. f(x) = f(v) = 1, F (x) = x and F (v) = v.
Q9. What is the difference between canonical and D-vines?
D-vines are more flexible than canonical vines, since for the canonical vines the authors specify the relationships between one specific pilot variable and the others, while in the D-vine structure the authors can select more freely which pairs to model.
Q10. What is the tail dependence of the Student’s t-copula?
The data clustering in the two opposite corners of these plots is a strong indication of both upper and lower tail dependence, meaning that the Student’s t-copula is an appropriate choice.
Q11. what is the log-likelihood of a dvine?
For the D-vine, the log-likelihood is given byn−1 ∑j=1n−j ∑i=1T ∑t=1log ( ci,i+j|i+1,...,i+j−1 (F (xi,t|xi+1,t, . . . , xi+j−1,t), F (xi+j,t|xi+1,t, . . . , xi+j−1,t)) ) .(17) The D-vine log-likelihood must also be numerically optimised.
Q12. What are the three important formulas for each of these four pair copulae?
In Appendix B the authors give three important formulas for each of these four pair copulae; the density, the h-function and the inverse of the h-function.