parcor<-function(x,y,t){
	rxy<-cor(x,y)
	rxt<-cor(x,t)
	ryt<-cor(y,t)
	num<-rxy-ryt*rxt
	denom<-sqrt(1-rxt*rxt)*sqrt(1-ryt*ryt)
	num/denom
}


########################################################################################
###################################Weekly Data##########################################
dax_w<-read.table("C:/Users/Chris/Documents/Stochastik III/R/dax_w.csv",header=T,sep=",")
dax_w_ret<-log(dax_w$Open[1:36])-log(dax_w$Open[2:37])
fre_w<-read.table("C:/Users/Chris/Documents/Stochastik III/R/fre_w.csv",header=T,sep=",")
fre_w_ret<-log(fre_w$Open[1:36])-log(fre_w$Open[2:37])
dai_w<-read.table("C:/Users/Chris/Documents/Stochastik III/R/dai_w.csv",header=T,sep=",")
dai_w_ret<-log(dai_w$Open[1:36])-log(dai_w$Open[2:37])
cor(cbind(fre_w_ret,dai_w_ret,dax_w_ret))
parcor(fre_w_ret,dai_w_ret,dax_w_ret)
parcor(dax_w_ret,dai_w_ret,fre_w_ret)
parcor(dax_w_ret,fre_w_ret,dai_w_ret)
sqrt(33)*(-0.1774293)/sqrt(1-0.1774293*0.1774293)
qt(0.975,df=33)
########################################################################################
#################################Studenten Beispiel#####################################
student<-read.table("C:/Users/Chris/Documents/Stochastik III/R/student.csv",header=T,sep=";")
qqnorm(student$Uebung)
qqline(student$Uebung)
hist(student$Uebung)
cor(cbind(student$Uebung,student$Klausur,student$Student),method="spearman")
parcor(student$Uebung,student$Klausur,student$Student)
parcor(student$Uebung,student$Student,student$Klausur)
parcor(student$Student,student$Klausur,student$Uebung)
cor.test(student$Uebung,student$Klausur,method="spearman")









#####Daily Data#####NOT required#####

dax<-read.table("C:/Users/Chris/Documents/Stochastik III/R/dax.csv",header=T,sep=",")
dax_ret<-log(dax$Open[2:256])-log(dax$Open[3:257])
bmw<-read.table("C:/Users/Chris/Documents/Stochastik III/R/bmw.csv",header=T,sep=",")
bmw_ret<-log(bmw$Open[1:255])-log(bmw$Open[2:256])
fre<-read.table("C:/Users/Chris/Documents/Stochastik III/R/fre.csv",header=T,sep=",")
fre_ret<-log(fre$Open[1:255])-log(fre$Open[2:256])
dai<-read.table("C:/Users/Chris/Documents/Stochastik III/R/dai.csv",header=T,sep=",")
dai_ret<-log(dai$Open[1:255])-log(dai$Open[2:256])
alv<-read.table("C:/Users/Chris/Documents/Stochastik III/R/alv.csv",header=T,sep=",")
alv_ret<-log(alv$Open[1:255])-log(alv$Open[2:256])
ads<-read.table("C:/Users/Chris/Documents/Stochastik III/R/ads.csv",header=T,sep=",")
ads_ret<-log(alv$Open[1:255])-log(alv$Open[2:256])

dax<-read.table("C:/Users/Chris/Documents/Stochastik III/R/dax.csv",header=T,sep=",")
dax_ret<-log(dax$Open[2:256])-log(dax$Open[3:257])
bmw<-read.table("C:/Users/Chris/Documents/Stochastik III/R/bmw.csv",header=T,sep=",")
bmw_ret<-log(bmw$Open[1:255])-log(bmw$Open[2:256])
cor.test(dax_ret,bmw_ret,method="spearman")

cor(cbind(alv_ret,dax_ret,dai_ret,fre_ret,bmw_ret,ads_ret))


#################Weekly Data###########################
bmw_w<-read.table("C:/Users/Chris/Documents/Stochastik III/R/bmw_w.csv",header=T,sep=",")
bmw_w_ret<-log(bmw_w$Open[1:36])-log(bmw_w$Open[2:37])
alv_w<-read.table("C:/Users/Chris/Documents/Stochastik III/R/alv_w.csv",header=T,sep=",")
alv_w_ret<-log(alv_w$Open[1:36])-log(alv_w$Open[2:37])
ads_w<-read.table("C:/Users/Chris/Documents/Stochastik III/R/ads_w.csv",header=T,sep=",")
ads_w_ret<-log(alv_w$Open[1:36])-log(alv_w$Open[2:37])