Eko <- read.csv("C:/Users/mpady/Desktop/SPY.csv",sep=";")
SPY<-Eko[5822:6073,1]
SPY<-as.numeric(gsub(",", ".", gsub("\\.", "", SPY)))
MA200<-Eko[5822:6073,2]
MA200<-as.numeric(gsub(",", ".", gsub("\\.", "",MA200)))
j<-rep(1,length(MA200))
X<-cbind(j,MA200)
n<-length(SPY)
Linmodel<-lm(SPY~MA200)
summary(Linmodel)
sigmahl<-summary(Linmodel)$sigma
#test normality rezidui
epsilonHAT<-SPY-X%*%Linmodel$coefficients
shapiro.test(epsilonHAT)
ks.test(epsilonHAT,"pnorm", mean=mean(epsilonHAT),sd=sqrt(var(epsilonHAT)))
#vykreslenie dat a regresnej krivky
plot(MA200,SPY)
abline(Linmodel$coefficients,col="red")
#CUSUM
# vypocet s^2 z celej vzorky
k<-length(Linmodel$coefficients)
SPYfitted<-X%*%solve(t(X)%*%X)%*%t(X)%*%SPY
RSS<-t(SPY-SPYfitted)%*%(SPY-SPYfitted)
s2<-RSS/(n-k)