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... [Read more...]

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... [Read more...]

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... [Read more...]

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-... [Read more...]

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

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... [Read more...]

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) __ ... [Read more...]

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... [Read more...]

Once again, I (re)discovered last week at the Rmetrics conference that old toolds can be extremely interesting to illustrate complex ideas, like uncertainty in fnancial markets, and stock prices. For instance a 99.5% quantile: we look for the scena... [Read more...]

This week, at the Rmetrics conference, there has been an interesting discussion about heuristic optimization. The starting point was simple: in complex optimization problems (here we mean with a lot of local maxima, for instance), we do not ne... [Read more...]

I will be giving a short course in Switzerland next week, at the 6th R/Rmetrics Meielisalp Workshop & Summer School on Computational Finance and Financial Engineering organized by ETH Zürich, https://www.rmetrics.org/. The long... [Read more...]

I am a big fan of trees. It is a very nice way to see how financial pricing works, for derivatives. An with a matrix-based language (R for instance), it is extremely simple to compute almost everything. Even multiple assets options. Let us see how ... [Read more...]

10 days ago, a study published on http://www.annalsofepidemiology.org/ mentioned that "Death has a preference for birthdays" (as claimed in the title). The conclusion of the paper is that, in general, birthdays do not evoke a postponement mechanism... [Read more...]

Last week, @3wen (Ewen) helped me to write nice R functions to extract tweets in R and build datasets containing a lot of information. I've tried a couple of time on my own. Once on tweet contents, but it was not convincing and once on the activit... [Read more...]

Following previous posts on life contingencies and longevity and mortality models, I upload additional material for the short course at the 6th R/Rmetrics Meielisalp Workshop & Summer School on Computational Finance and Financial Engineeri... [Read more...]

Following the previous post on life contingencies and actuarial models in life insurance, I upload additional material for the short course at the 6th R/Rmetrics Meielisalp Workshop & Summer School on Computational Finance and Financial Engineering organized by ETH Zürich, https://www.rmetrics.org/. The second part of the ... [Read more...]

I will be giving in less than four weeks a short course at the 6th R/Rmetrics Meielisalp Workshop & Summer School on Computational Finance and Financial Engineering organized by ETH Zürich, https://www.rmetrics.org/. The talk will be on Actuarial models with R, and first part will be ... [Read more...]

A short post today based on recent work by @3wen (Ewen Galic, graduate Student in Rennes, spending a year in Montreal). Since we were working on a detailed French dataset (per commune), we needed a dataset containing a list all communes, with popu... [Read more...]

This week, I have seen on the internet (sorry, I cannot find proper references) the graph produced here on the right: which birthday is most likely ? The fact that I have no further information is important, since I do not know in which country suc... [Read more...]

Dependence in dimension 2 is difficult. But one has to admit that dimension 2 is way more simple than dimension 3 ! I recently rediscovered a nice paper, Langford, Schwertman & Owens (2001), on transitivity of the property of being positively c... [Read more...]