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5

Here is a working paper that you may be interested in.


3

I found Coping With Copulas by Thorsten Schmidt really helped me to get a more basic understanding of copulas. As well as looking at some simple examples in R and thinking about different directions the transformations can happen. To answer your actual question I'll attempt to describe the steps involved as simply as I can. Let's say you use the copula ...


2

The best introduction to copulas I know, i.e. with rigour and intuition, is the following. THE QUANT CLASSROOM BY ATTILIO MEUCCI A Short, Comprehensive, Practical Guide to Copulas Visually introducing a powerful risk management tool to generalize and stress-test correlations


2

Do you refer with 'negative tail dependence' to the case that one variable has a extremely low value and the other random variable has an extremely large value, i.e., $$\tau=\lim_{p \rightarrow 0} \frac{Pr[x>Q_x(1-p),y<Q_y(p)]}{p},$$ where $Q_x(1-p)$ and $Q_y(p)$ refer to the $(1-p)$-th quantile of the random variable $x$ and the $p$-th quantile of ...


2

The answer of user27915816 led me into the right direction, yet I think I found an even better generalization: Distance Correlation (dCor) There are several reasons for that: It generalizes classical (i.e. linear) correlation in the sense that linearity is a special case. It gives identical readings for linear dependence. There are analogs for variance, ...


2

Mutual information measures how much knowing one variable reduces uncertainty about another variable. It considers any type of dependency (linear or non-linear), it's measured in bits, and it is widely used in machine learning, computer vision NLP and other fields.


2

In the theory of copulas you want to model a multivariate (often bivariate) distribution and keep the marginals fixed. Thus you have random variables $X$ and $Y$ with cdf $F_X(x) = P[X \le x]$ and $F_Y(y) = P[Y\le y]$ and you want to find some $F_{X,Y}(x,y) = P[X \le x, Y\le y]$ such that when you look at marginals you get $F_{X,Y}(x,\infty) = F_X(x)$ and ...


1

There is a brief and not overly technical introduction here: http://prescientmuse.blogspot.co.uk/2015/01/a-brief-introduction-to-copula.html And an application of use in a trading system with full R code here: http://prescientmuse.blogspot.co.uk/2015/02/vanilla-trading-algorithm.html Hope that helps!



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