Flashcards in Part 3 Deck (10):
Main advantage of copula fn over joint distr
- In many situation, when MD aren't Gaussian, it is impossible to define a joint distr
- This is the case when 2 variables have diff MD
- In addition, a lot of MD don't have a multivariate extension
- Sol: copula fns: they have the property to relate 2 MD instead 2 series directly
If non-normal returns, when is MV criterion good?
If MV investor, nothing has to be changed in case of non-normality
Advantages and drawbacks of elliptical vs Archimedean copulas
- Adv of Archimedean: most of them have closed form expression
- Drawback of Archimedean: their multivariate extensions are difficult to establish
Why Pearson's corr coeff not good to measure concordance?
- Measure of association but not necessarily of concordance
- Concordance only under normality
- Pearson's corr is a natural scalar measure of linear dependence in elliptical distributions
- BUT may be misleading in more general situations
Relation btw cdf of joint distr fn and corresponding copula (Sklar theorem)
- Sklar: let H be joint distr fn of X,Y with MDs F,G
- Then, there exists a copula C:(0,1)*(0,1) -> (0,1) s.t. H(x,y)=C(F(x),G(y))
- Furthermore, if F and G are continuous, C is unique
Why is 2-step estimation consistent with copula?
- Since MLE may be difficult to implement, in some cases, the vector of parameters can be split in 2 diff parts: those associated with the margins and with the copula:
1) Estimation of the margins
2) Estimation of the parameters teta_gamma of the copula model conditionally on the margin parameter
How use method of moments for estimating copula parameters?
- Let consider a concordance measure (Kendall's tau or Spearman's rho) which can be easily estimated as a fn of the copula parameters
- Then, an estimation of the parameter is obtained by equalizing the theoretical and empirical quantities
Why Kendall's tau better measure of dependence than Pearson's corr coeff
- Pearson's corr is a valid measure for linear dependence within the elliptical family of distr
- Kendall's tau also captures non-linear associations
Used to describe deviations from normality of innovations in à GARCH framework