Blog Archives

Copulas and tail dependence, part 3

September 18, 2012
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Copulas and tail dependence, part 3

We have seen extreme value copulas in the section where we did consider general families of copulas. In the bivariate case, an extreme value can be writtenwhere is Pickands dependence function, which is a convex function satisfyingObserve that in ...

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Copulas and tail dependence, part 2

September 18, 2012
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Copulas and tail dependence, part 2

An alternative to describe tail dependence can be found in the Ledford & Tawn (1996) for instance. The intuition behind can be found in Fischer & Klein (2007)). Assume that and have the same distribution. Now, if we assume that those vari...

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Copulas and tail dependence, part 1

September 17, 2012
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Copulas and tail dependence, part 1

As mentioned in the course last week Venter (2003) suggested nice functions to illustrate tail dependence (see also some slides used in Berlin a few years ago). Joe (1990)'s lambda Joe (1990) suggested a (strong) tail dependence index. For lower t...

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Kendall’s function for copulas

September 12, 2012
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Kendall’s function for copulas

As mentioned in the course on copulas, a nice tool to describe dependence it Kendall's cumulative function. Given a random pair with distribution  , define random variable . Then Kendall's cumulative function is Genest and Rivest (1993) intr...

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Association and concordance measures

September 12, 2012
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Association and concordance measures

Following the course, in order to define assocation measures (from Kruskal (1958)) or concordance measures (from Scarsini (1984)), define a concordance function as follows: let be a random pair with copula , and with copula . Then define the so-...

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Unit root, or not ? is it a big deal ?

September 10, 2012
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Unit root, or not ? is it a big deal ?

Consider a time series, generated using set.seed(1) E=rnorm(240) X=rep(NA,240) rho=0.8 X=0 for(t in 2:240){X=rho*X+E} The idea is to assume that an autoregressive model can be considered, but we don't know the value of the parameter. ...

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That damn R-squared !

September 7, 2012
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That damn R-squared !

Another post about the R-squared coefficient, and about why, after some years teaching econometrics, I still hate when students ask questions about it. Usually, it starts with "I have a _____ R-squared... isn't it too low ?" Please, feel free to fi...

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Inference and autoregressive processes

September 6, 2012
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Inference and autoregressive processes

Consider a (stationary) autoregressive process, say of order 2, for some white noise with variance . Here is a code to generate such a process, > phi1=.5 > phi2=-.4 > sigma=1.5 > set.seed(1) > n=240 > WN=rnorm(n,sd=sigma) > ...

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Border bias and weighted kernels

August 31, 2012
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Border bias and weighted kernels

With Ewen (aka @3wen), not only we have been playing on Twitter this month, we have also been working on kernel estimation for densities of spatial processes. Actually, it is only a part of what he was working on, but that part on kernel estimation...

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Border bias and weighted kernels

August 31, 2012
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Border bias and weighted kernels

With Ewen (aka @3wen), not only we have been playing on Twitter this month, we have also been working on kernel estimation for densities of spatial processes. Actually, it is only a part of what he was working on, but that part on kernel estimation has been the opportunity to write a short paper, that can now be downloaded on hal. The problem...

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