hw1_ex1

rm(list=ls())
#install package "quantmod"
library(quantmod)

## Loading required package: xts

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## Loading required package: TTR

## Version 0.4-0 included new data defaults. See ?getSymbols.

library(fBasics)

## Loading required package: timeDate

## Loading required package: timeSeries

## 
## Attaching package: 'timeSeries'

## The following object is masked from 'package:zoo':
## 
##     time<-

## 
## Attaching package: 'fBasics'

## The following object is masked from 'package:TTR':
## 
##     volatility

da=read.table("d-axp3dx-0111.txt",header=T)
head(da)

##       date       axp        vw        ew        sp
## 1 20010904  0.000824 -0.001658 -0.005708 -0.000565
## 2 20010905  0.007682 -0.003242 -0.008926 -0.001059
## 3 20010906 -0.039477 -0.020733 -0.014187 -0.022390
## 4 20010907 -0.019274 -0.017769 -0.011476 -0.018637
## 5 20010910  0.011850  0.003513 -0.007368  0.006226
## 6 20010917 -0.135961 -0.050714 -0.042398 -0.049216

axp3dx=da[,2]
basicStats(axp3dx)

##                  axp3dx
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.175949
## Maximum        0.206485
## 1. Quartile   -0.009672
## 3. Quartile    0.010540
## Mean           0.000534
## Median         0.000000
## Sum            1.353560
## SE Mean        0.000524
## LCL Mean      -0.000493
## UCL Mean       0.001561
## Variance       0.000695
## Stdev          0.026368
## Skewness       0.459773
## Kurtosis       9.592053

mean(axp3dx) 

## [1] 0.0005339487

stdev(axp3dx)

## [1] 0.02636841

skewness(axp3dx)

## [1] 0.4597734
## attr(,"method")
## [1] "moment"

kurtosis(axp3dx)

## [1] 9.592053
## attr(,"method")
## [1] "excess"

#===================================
#transform simplereturn into log return
#===================================
da=read.table("d-axp3dx-0111.txt",header=T)
head(da)

##       date       axp        vw        ew        sp
## 1 20010904  0.000824 -0.001658 -0.005708 -0.000565
## 2 20010905  0.007682 -0.003242 -0.008926 -0.001059
## 3 20010906 -0.039477 -0.020733 -0.014187 -0.022390
## 4 20010907 -0.019274 -0.017769 -0.011476 -0.018637
## 5 20010910  0.011850  0.003513 -0.007368  0.006226
## 6 20010917 -0.135961 -0.050714 -0.042398 -0.049216

axp=log(da$axp+1)
basicStats(axp)

##                     axp
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.193523
## Maximum        0.187711
## 1. Quartile   -0.009719
## 3. Quartile    0.010484
## Mean           0.000188
## Median         0.000000
## Sum            0.476584
## SE Mean        0.000522
## LCL Mean      -0.000836
## UCL Mean       0.001212
## Variance       0.000691
## Stdev          0.026294
## Skewness       0.020992
## Kurtosis       9.020499

vw=log(da$axp+1)
basicStats(vw)

##                      vw
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.193523
## Maximum        0.187711
## 1. Quartile   -0.009719
## 3. Quartile    0.010484
## Mean           0.000188
## Median         0.000000
## Sum            0.476584
## SE Mean        0.000522
## LCL Mean      -0.000836
## UCL Mean       0.001212
## Variance       0.000691
## Stdev          0.026294
## Skewness       0.020992
## Kurtosis       9.020499

ew=log(da$axp+1)
basicStats(ew)

##                      ew
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.193523
## Maximum        0.187711
## 1. Quartile   -0.009719
## 3. Quartile    0.010484
## Mean           0.000188
## Median         0.000000
## Sum            0.476584
## SE Mean        0.000522
## LCL Mean      -0.000836
## UCL Mean       0.001212
## Variance       0.000691
## Stdev          0.026294
## Skewness       0.020992
## Kurtosis       9.020499

sp=log(da$axp+1)
basicStats(sp)

##                      sp
## nobs        2535.000000
## NAs            0.000000
## Minimum       -0.193523
## Maximum        0.187711
## 1. Quartile   -0.009719
## 3. Quartile    0.010484
## Mean           0.000188
## Median         0.000000
## Sum            0.476584
## SE Mean        0.000522
## LCL Mean      -0.000836
## UCL Mean       0.001212
## Variance       0.000691
## Stdev          0.026294
## Skewness       0.020992
## Kurtosis       9.020499

#=======================
#null hypothesis
#===========================
library(fBasics)
da=read.table("d-axp3dx-0111.txt",header=T) 
axp=da[,2] 
hist(axp,nclass=30) 

d1=density(axp) 
range(axp) 

## [1] -0.175949  0.206485

x=seq(-.1,.1,.001) 
y1=dnorm(x,mean(axp),stdev(axp))
plot(d1$x,d1$y,xlab="rtn",ylab="density",type="l")
lines(x,y1,lty=2)