#Some functions for the ESSRES statistic lecture
#Handle with care, they are basically untested. tlaepple@awi.de 12.May.09

#Blocksampling with given blocklength
blocksample<-function(data,blocklength=10)
{
	nblock<-ceiling(length(data)/blocklength) #Determine how many blocks we need
	starts<-floor(runif(nblock,min=1,max=length(data)-blocklength+1)) #random startpoints of the blocks
	index<-rep(1:blocklength,nblock) + rep(starts,each=blocklength)   #create an index vector containing all blocks
	return(data[index[1:length(data)]]) #Only keep length(data) points
}

#Effective DOF
dof.effective<-function(n,a1) 
{
	return(n/(1+2/n*1/(1-a1)*(a1*(n-1/(1-a1))-a1^n*(1-1/(1-a1)))))
}

#Optimal block length
lopt<-function(n,a1) 
{
	return(ceiling((6^(0.5)*a1/(1-a1)^2)^(2/3)*n^(1/3)))
}

#lag-1 scatterplot
lagscatterplot<-function(data,...)
{
	plot(data[-1],data[-length(data)],xlab="",ylab="",pch=20, ...)
	abline(a=0,b=1,lwd=2,col="grey")
}