#Q1. This problem uses the data set ford.csv on the book’s web site.
#The data were taken from the ford.s data set in R’s fEcofin package.
#This package is no longer on CRAN.
#This data set contains 2000 daily Ford returns from January 2, 1984, to December 31, 1991.
rm(list = ls())
con = gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb'))
source(con)
close(con)
library(tidyverse)
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library(quantmod)
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library(plyr)
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library(fBasics)
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library(fEcofin)
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#install.packages(fEcofin)
data(ford.s , package = "fEcofin")
tail(ford.s)
## X.m..d..y FORD
## 1995 12/23/1991 0.103960400
## 1996 12/24/1991 0.008968610
## 1997 12/26/1991 0.008888889
## 1998 12/27/1991 -0.022026430
## 1999 12/30/1991 0.018018020
## 2000 12/31/1991 -0.004424779
#(a) Find the sample mean, sample median, and standard deviation of the Ford returns.
ford.return = ford.s$FORD
ford.matrix = as.matrix(ford.return)
mean = mean(ford.return)
mean
## [1] 0.0007600789
median = median(rnorm(ford.matrix))
median
## [1] 0.01707339
sd = sd(ford.matrix)
sd
## [1] 0.01831557
#(b) Create a normal plot of the Ford returns.
#Do the returns look normally distributed? If not, how do they differ from being normally distributed?
n = length(ford.return)
year_SP = 1984 + (1:n) * (1991.25 - 1984) / n
plot(year_SP, ford.return, main = "Ford daily returns",
xlab = "year", type = "l", ylab = "log return")
plot(as.data.frame(ford.return))
hist(ford.return, 80, freq= FALSE)
hist(ford.return)
plot(as.data.frame(ford.return))
hist(ford.return, 80, freq= FALSE)
hist(ford.return)
hist(ford.return)
#(c) Test for normality using the Shapiro–Wilk test? What is the p-value?
#Can you reject the null hypothes is of a normal distribution at 0.01?
sh <- shapiro.test(ford.return) # Shapiro--Wilk
sh
##
## Shapiro-Wilk normality test
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## data: ford.return
## W = 0.96388, p-value < 2.2e-16
# p- value = 2.2e-16 = 0.00000000000000022 means less than 0.05. Therefore it can not reject null hypothes, even at 0.01.
# In other word it is not normally distributed.
#(d) Create several t-plots of the Ford returns using a number of choices of the degrees of freedom parameter
n=dim(ford.matrix)[1]
q_grid = (1:n) / (n + 1)
df_grid = c(1, 4, 6, 10, 20, 30)
index.names = dimnames(ford.matrix)[[2]]
for(i in 1:1){
#dev.new()
par(mfrow = c(3, 2))
for(df in df_grid){
qqplot(ford.matrix[,i], qt(q_grid,df),
main = paste(index.names[,i], ", df = ", df) )
abline(lm(qt(c(0.25, 0.75), df = df) ~
quantile(ford.matrix[,i], c(0.25, 0.75))))} }
#(f) What value of df gives a plot that is as linear as possible?
#The returns include the return on Black Monday, October 19, 1987.
#Discuss whether or not to ignore that return when looking for the best choices of df.
# If df=6 it is linear as possible