Blog Archives

There is no “Too Big” Data, is there?

April 23, 2014
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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...

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How Fast the Fastest Human Would Run 100m?

April 16, 2014
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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...

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Computational Actuarial Science

April 6, 2014
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Computational Actuarial Science

Last week, we’ve been through the book, completely, one last time, before sending it back to the publisher, with some comments and remarks, before publication ! So, this is it, the book will finally appear soon ! It was schedule for this week actually, but… you know. It should appear sometime by the end of May, or beginning of...

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Stationarity of ARCH processes

April 6, 2014
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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 infinite number...

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Inference for ARCH processes

April 2, 2014
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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=w+a1*epsilon^2+a2*epsilon^2 + epsilon=eta*sqrt(sigma2) + } > par(mfrow=c(1,1)) > plot(epsilon,type="l",ylim=c(min(epsilon)-.5,max(epsilon))) > lines(min(epsilon)-1+sqrt(sigma2),col="red") (the red line is the conditional variance process). > par(mfrow=c(1,2)) > acf(epsilon,lag=50,lwd=2)...

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Modeling the Marginals and the Dependence separately

April 1, 2014
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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 generate a multivariate cumulative distribution function with...

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Correlation with constraints on pairs

March 31, 2014
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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 markets). More precisely, if one knows the...

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Seasonal Unit Roots

March 26, 2014
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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...

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Seasonal, or periodic, time series

March 20, 2014
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Seasonal, or periodic, time series

Monday, in our MAT8181 class, we’ve discussed seasonal unit roots from a practical perspective (the theory will be briefly mentioned in a few weeks, once we’ve seen multivariate models). Consider some time series , for instance traffic on French roads, > autoroute=read.table( + "http://freakonometrics.blog.free.fr/public/data/autoroute.csv", + header=TRUE,sep=";") > X=autoroute$a100 > T=1:length(X) > plot(T,X,type="l",xlim=c(0,120)) > reg=lm(X~T) > abline(reg,col="red") As discussed in a...

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Moving the North Pole to the Equator

March 15, 2014
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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()...

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