0.1 《Analysis of Financial Time Series》p10 1-2-1

考虑数据中 IBM 股票的日简单收益率，检验收益率是否服从正态分布。

library(fBasics)
setwd("D:\\New_Folder\\Study_Programming\\R_Programme\\R-Financial-Time-Series\\Tsay3 data")
da=read.table("d-ibm3dx7008.txt",header=T) 
    # header=T 表示第一行为变量名称，如果不这么设置（header=F），那么需要重新定义变量名称
dim(da) # Find size of 'da',共9845行数据，5个变量
## [1] 9845    5
da[1,] # See the firSt row of the data.
##       Date      rtn   vwretd  ewretd   sprtrn
## 1 19700102 0.000686 0.012137 0.03345 0.010211
ibm=da[,2] # Obtain IBM simple returns.
sibm=ibm*100 # Percentage simple returns.
basicStats(sibm) # basicStats:基本统计量
##                    sibm
## nobs        9845.000000
## NAs            0.000000
## Minimum      -22.963000
## Maximum       13.163600
## 1. Quartile   -0.857100
## 3. Quartile    0.883300
## Mean           0.040161
## Median         0.000000
## Sum          395.387600
## SE Mean        0.017058
## LCL Mean       0.006724
## UCL Mean       0.073599
## Variance       2.864705
## Stdev          1.692544
## Skewness       0.061399
## Kurtosis       9.916359

0.1.1 正态性检验：

s1=skewness(sibm)
t1=s1/sqrt(6/dim(da)[1]) # Compute the test statistic 检验统计量
t1
## [1] 2.487093
## attr(,"method")
## [1] "moment"
pv=2*(1-pnorm(t1)) # Compute t-value
pv
## [1] 0.01287919
## attr(,"method")
## [1] "moment"
libm=log(ibm+1)*100 # Turn to log returns in percentages.
# libm: percentage of log return  
t.test(libm) # t.test: test H0:if libm is zero  
## 
##  One Sample t-test
## 
## data:  libm
## t = 1.5126, df = 9844, p-value = 0.1304
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.007641473  0.059290531
## sample estimates:
##  mean of x 
## 0.02582453

结果显示p值>0.05，不能拒绝原假设

indicating that the daily simple returns of IBM stock are significantly skewed to the right at the 5% level.

normalTest(libm,method = 'jb') # JB statistics in testing normality
## 
## Title:
##  Jarque - Bera Normalality Test
## 
## Test Results:
##   STATISTIC:
##     X-squared: 60921.9343
##   P VALUE:
##     Asymptotic p Value: < 2.2e-16

结果显示p值<0.05,拒绝原假设，即不服从正态性。

(From the output, the excess kurtosis is high, indicating that the daily simple returns of IBM stock have heavy tails.)