datafiles<- read.table("SPXdata.csv", header = TRUE, sep = ",", na.string=".") 
SPX<-datafiles[1]

Y<-data.frame(SPX)
par(mfrow = c(1,1))
xname<-"S&P Daily Returns (2005-2009)"
hist(Y$SPX,breaks = "FD",main = paste("Histogram of" , xname),xlab = xname)


###############################
xname<-"S&P Daily Returns (2005-2009)"
par(mfrow = c(1,1))
plot(density(Y$SPX, bw="ucv",kernel = "epanechnikov"),main = paste("Density Estimation of" , xname),xlab = xname)
#X<-seq(min(Y$SPX), max(Y$SPX), length=length(Y$SPX))


y<-Y$SPX

simpson <- function(x, y){
n <- length(y)
odd <- n %% 2
if (odd) area <- 1/3*sum( y[1] + 2*sum(y[seq(3,(n-2),by=2)]) +
        4*sum(y[seq(2,(n-1),by=2)]) + y[n])

if (!odd) area <- 1/3*sum( y[1] + 2*sum(y[seq(3,(n-3),by=2)]) +
        4*sum(y[seq(2,(n-2),by=2)]) + y[n-1]) + 1/2*(y[n-1] + y[n])

dx <- x[2] - x[1]
return(area * dx)
}

simpson(x, y)