Blog Archives

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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Identification of ARMA processes

February 19, 2014
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Identification of ARMA processes

Last week (in the MAT8181 course) in order to identify the orders of an ARMA process, we’ve seen the eacf method, and I mentioned the scan method, introduced in Tsay and Tiao (1985). The code below – to produce the output of the scan procedure – has been adapted from an old code by Steve Chen (where I included a visualization...

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Voting Twice in France

February 19, 2014
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Voting Twice in France

On the Monkey Cage blog, Baptiste Coulmont (a.k.a. @coulmont) recently uploaded a post entitled “You can vote twice ! The many political appeals of proxy votes in France“, coauthored with Joël Gombin (a.k.a. @joelgombin), and myself. The study was initially written in French as mentioned in a previous post. Baptiste posted additional information on his blog (http://coulmont.com/blog/…) and I also wanted to post some lines of code,...

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Bivariate Densities with N(0,1) Margins

February 18, 2014
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Bivariate Densities with N(0,1) Margins

This Monday, in the ACT8595 course, we came back on elliptical distributions and conditional independence (here is an old post on de Finetti’s theorem, and the extension to Hewitt-Savage’s). I have shown simulations, to illustrate those two concepts of dependent variables, but I wanted to spend some time to visualize densities. More specifically what could be the joint density...

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Temperatures Series as Random Walks

February 12, 2014
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Temperatures Series as Random Walks

Last year, I did mention in a post that unit-root tests are dangerous, because they might lead us to strange models. For instance, in a post, I did obtain that the temperature observed in January 2013, in Montréal, might be considered as a random walk process (or at leat an integrated process). The code to extract the data has...

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Unit Root Tests

February 12, 2014
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Unit Root Tests

This week, in the MAT8181 Time Series course, we’ve discussed unit root tests. According to Wold’s theorem, if is  (weakly) stationnary then where is the innovation process, and where  is some deterministic series (just to get a result as general as possible). Observe that as discussed in a previous post. To go one step further, there is also the...

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