Via @theEconomist, I understood that there might be connections between the price of Gold (which is said to be extremely high nowadays) and the VIX SP500 index (the option volatility index, i.e. the so-called “fear index“, as discussed – in French- a few months ago). This has been discussed also on several blogs, e.g. http://etfdailynews.com/ or http://blogs.marketwatch.com/. Via Yahoo quotes, it is possible to get also easily the
SP500 VIX index.
> library(tseries) > X=get.hist.quote("^VIX") > T=time(VIX) > Y=as.POSIXlt(T)$year+1900 > X2011=X[Y==2011,] > VIX=X2011[,4] > VIX100=as.numeric(VIX)/VIX[1]*100 > T2011=T[Y==2011] > plot(T2011,VIX100,lwd=2,col="red",type="l", + xlab="",ylab="",ylim=c(60,290))
And a huge xls file can give us the price of gold (on a daily basis). But we can extract only one series (with the price in USD, which is the series of interest here)
> goldprice=read.table( + "http://freakonometrics.blog.free.fr/ public/data/goldpriceUSD.csv", + header=TRUE,sep=";",dec=",") > T=as.Date(goldprice$Name,"%d/%m/%y") > GP=goldprice$USdollar > Y=as.POSIXlt(T)$year+1896 > GP2011=GP[Y==2011] > GP100=GP2011/GP2011[1]*100 > T2011=T[Y==2011] > lines(T2011-4*365.25,GP100,lwd=2,col="blue")
We can see that scales are quite different on those two series (starting at 100 at the beginning of January 2011),

An alternative might be not to consider the price of gold, but something more psychological, like Internet researches. It is possible to download the csv file for queries on gold price on Google, via google insight.
> google=read.table( + "http://freakonometrics.blog.free.fr/public/data/google.csv", + skip=4,header=TRUE,sep=",",nrows=51) > W=as.Date(substr(as.character(google$Semaine),1,10)) > G=google$gold.price > G100=G/G[1]*100 > lines(W,G100,lwd=2,col="blue")
which gives the following graph (again, starting at 100 at the beginning of January 2011),

Here, we can clearly observe that the two series are related, maybe cointegrated. Nice isn’t it ?
était un estimateur Gaussien. En particulier, chacun des estimateurs est alors Gaussien, au sens où
, ce qui peut se visualiser sur le graphique suivant (la constante est en abscisse, et la pente en ordonnée), avec un intervalle de confiance à 95%,








such that
where
‘s are i.i.d. with cumulative distribution function
. They had supporting arguments, but no (rigorous) proof. Nevertheless, the obtained that the only possible types for G were



as possible limit. Richard von Mises gave in 1936 sufficient, but not necessary conditions for their (max) domain of attraction, i.e. characterization of function
such that the maxima converges to some specific function 
is regularly varying at infinity, with index
(even if the term “regular variation” was not mentioned in the paper). Similar results were derived to characterize functions in the (max) domain of attraction of Weibull. For the (max) domain of attraction of
, Boris Gnedenko obtained that a necessary and sufficient condition was that there exists a function
such 




(with a much shorter proof).