## Stock PC analysis
## AHW3
## Decmeber 4, 2007

rm(list = ls())

## read in data
stock <- read.table("stock.txt", header=T)
n <- nrow(stock)
p <- ncol(stock)

## plot the data
par(mfrow=c(5,1))
for(i in 1:p){
plot(stock[,i], type="l", lwd=2, ylab=names(stock)[i], xlab="return", col=i, cex.lab=1.5)
}

par(mfrow=c(1,1))
plot(stock[,1], type="l", lwd=2, ylab="Stocks", col=1, cex.lab=1.5)
for(i in 2:p){
lines(stock[,i], type="l", lwd=2, col=i)
}

par(mfrow=c(1,1))
pairs(stock)

## get sample mean, cov, cor
stock.m <- round(apply(stock, 2, mean),4)
stock.m

stock.S <- round(cov(stock),5)
stock.S

stock.R <- round(cor(stock),3)
stock.R


## get the principle components using the correlation matrix
pc <- eigen(stock.S)
pc

## proportion of variance explained by each component
pc$values/sum(pc$values)

## added proportion of variance explained by each component
cumsum(pc$values)/sum(pc$values)

## look at the scree plot
plot(1:5, pc$values, type="l", main="Scree Plot")
points(1:5, pc$values, col="blue", pch=16)

## from the plot 3 components seem sufficient 


## get the principle components using the correlation matrix
pc <- eigen(stock.R)
pc

## proportion of variance explained by each component
pc$values/sum(pc$values)

## added proportion of variance explained by each component
cumsum(pc$values)/sum(pc$values)

## look at the scree plot
plot(1:5, pc$values, type="l", main="Scree Plot")
points(1:5, pc$values, col="blue", pch=16)

## from the plot 3 components seem sufficient