Publications by arthur charpentier
Moving the North Pole to the Equator
I am still working with @3wen on visualizations of the North Pole. So far, it was not that difficult to generate maps, but we started to have problems with the ice region in the Arctic. More precisely, it was complicated to compute the area of this region (even if we can easily get a shapefile). Consider the globe, worldmap <- ggplot() + geom_...
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Seasonal Unit Roots
As discussed in the MAT8181 course, there are – at least – two kinds of non-stationary time series: those with a trend, and those with a unit-root (they will be called integrated). Unit root tests cannot be used to assess whether a time series is stationary, or not. They can only detect integrated time series. And the same holds for seasonal...
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Correlation with constraints on pairs
An interesting question was posted on http://math.stackexchange.com/726205/…: if one knows the covariances and , is it possible to infer ? I asked myself a question close to this one a few weeks ago (that I might also relate to a question I asked a long time ago, about possible correlations between three exchange rates, on financial marke...
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Modeling the Marginals and the Dependence separately
When introducing copulas, it is commonly admitted that copulas are interesting because they allow to model the marginals and the dependence structure separately. The motivation is probably Sklar’s theorem, which says that given some marginal cumulative distribution functions (say and , in dimension 2), and a copula (denoted ), then we can gen...
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Inference for ARCH processes
Consider some ARCH() process, say ARCH(), where with a Gaussian (strong) white noise . > n=500 > a1=0.8 > a2=0.0 > w= 0.2 > set.seed(1) > eta=rnorm(n) > epsilon=rnorm(n) > sigma2=rep(w,n) > for(t in 3:n){ + sigma2[t]=w+a1*epsilon[t-1]^2+a2*epsilon[t-2]^2 + epsilon[t]=eta[t]*sqrt(sigma2[t]) + } > par(mfrow=c(1,1)) > plot(epsilon,type="l",ylim=c(...
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Stationarity of ARCH processes
In the context of AR(1) processes, we spent some time to explain what happens when is close to 1. if the process is stationary, if the process is a random walk if the process will explode Again, random walks are extremely interesting processes, with puzzling properties. For instance, as , and the process will cross the x-axis an infin...
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How Fast the Fastest Human Would Run 100m?
Ethan Siegel wrote a post entitled The Math of the Fastest Human Alive five years ago, using regressions. An alternative is too use extreme value models (I wrote a post a long time ago on the maximum length of a tennis match using extreme value theory a few years ago). In 2009, John Einmahl and Sander Smeets wrote a great article entitled ultim...
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There is no “Too Big” Data, is there?
A few years ago, a former classmate came back to me with a simple problem. He was working for some insurance company (and still is, don’t worry, chatting with me is not yet a reason for dismissal), and his problem was that their dataset was too large to run (standard) codes to get a regression, and some predictions. My answer was too use sub-sa...
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Computational Actuarial Science
After some delay, the book Computational Actuarial Science with R is now annonced for July 2014. I don’t know if we will be able to get copies for the R in Insurance conference, in London, but I guess everyone is working on it. And kindly, CRC sent me the following flyer, with some reduction code to save 20% (when ordering on CRC’s website)....
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Allez les Bleus !
In almost three weeks, the (FIFA) World Cup will start, in Brazil. I have to admit that I am not a big fan of soccer, so I will not talk to much about it. Actually, I wanted to talk about colors, and variations on some colors. For instance, there are a lot of blues. In order to visualize standard blues, let us consider the following figure, inspi...
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