A few days ago, a former student of mine, David, contacted me about Box-Cox tests in linear models. It made me look more carefully at the test, and I do not understand what is computed, to be honest. Let us start with something simple, like a linea... [Read more...]

(bis repetita) Consider the following regression summary,Call: lm(formula = y1 ~ x1)   Coefficients: Estimate Std. Error t value Pr(__|t|) (Intercept) 3.0001 1.1247 2.667 0.02573 * x1 0.5001 0.1179 4.241 0.00217 **... [Read more...]

A few years ago, I went to listen to Roger Nelsen who was giving a talk about copulas with fractal support. Roger is amazing when he gives a talk (I am also a huge fan of his books, and articles), and I really wanted to play with that concept ... [Read more...]

Yesterday, I was asked how to write a code to generate a compound Poisson variables, i.e. a series of random variables  where  is a counting random variable (here Poisson disributed) and where the 's are i.i.d (and ind... [Read more...]

Consider our loss-ALAE dataset, and - as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, __ library(evd) __ data(lossalae) __ Z=lossalae __ X=Z[,1];Y=Z[,2] ... [Read more...]

Following the course of this afternoon, I will just upload some codes to make interactive 3d plots, in R. __ library(rgl) __ library(evd); __ data(lossalae) __ U=rank(lossalae[,1]+rnorm(nrow(lossalae), + mean=0,sd=.001))/(nrow(lossalae)+1) ... [Read more...]

Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related things).  Consider (as before) the loss-ALAE data... [Read more...]

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 ... [Read more...]

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...]