## First R lab - 2/04/2026

#install.packages(" ")
#load packages
library(quantmod)
library(moments)
library(tseries)

## download SP500 data from Yahoo Finance 
getSymbols("^GSPC", src="yahoo", 
           from="2000-01-02", 
           to="2016-12-31")
sp500<-GSPC
head(sp500)
dim(sp500)

# adjusted closing prices
adj_p<-sp500$GSPC.Adjusted
#View(adj_p)
class(adj_p)
plot(adj_p)

# import data from "sp500.csv"
# Index<-read.csv("sp500.csv")
# import data from .RData
# load("Index.RData")

#extract prices as a vector
It<-as.vector(adj_p$GSPC.Adjusted)
head(It)
str(It)
# construct log-returns
rt<-diff(log(It))
str(rt)
N<-length(rt)
plot(rt, type = "l", col=2, main="Log-returns")

## exploratory data analysis

hist(rt, freq=FALSE, breaks = 30)
curve(dnorm(x, mean(rt), sd(rt)), add=TRUE, col="red", lwd=2)
#qq plot
qqnorm(rt, datax = TRUE)
qqline(rt, datax = TRUE)

summary(rt)
skewness(rt)
kurtosis(rt)-3
# testing for normality
jarque.bera.test(rt)

## investigate presence of autocorrelation
# Ljung-Box test and sample ACF

Box.test(rt, lag=15, type="Ljung-Box")
acf(rt)