#======================================================================================
#                         Loading the libraries                               #
#======================================================================================
library(tseries)
library(ggplot2)
library(gridExtra)
#======================================================================================
#                         Loading the data                                     #
#======================================================================================
data1 = read.csv("GSPC.csv")
data1$Date = as.Date(data1$Date, "%Y-%m-%d")
str(data1)

#======================================================================================
#                         Create return series                                  #
#======================================================================================
# Number of total observations
n = dim(data1)[1]

# define the return series
returns = log(data1$Close[2:n]) - log(data1$Close[1:(n-1)])

# extract dates into a variable and make a new dataframe
dates = data1$Date[-1]
data = data.frame(dates = dates, returns = returns)

# plot returns series
plot(dates, returns, type = 'l')

2. Let X and be two i.i.d. Bernoulli(e) random variables (taking I...