Return Calculus R

price4<- span=""> read.table('price4.txt',header = T)
price4[1:3,]

##   x5202 x7272 x4927 x4502
## 1    55   682  2460  3595
## 2    56   672  2543  3575
## 3    56   668  2544  3570

summary(price4)

##      x5202           x7272            x4927          x4502     
##  Min.   : 55.0   Min.   : 668.0   Min.   :2363   Min.   :3500  
##  1st Qu.: 73.0   1st Qu.: 780.0   1st Qu.:2467   1st Qu.:3710  
##  Median : 96.0   Median : 948.0   Median :2525   Median :3865  
##  Mean   : 92.4   Mean   : 968.8   Mean   :2633   Mean   :4199  
##  3rd Qu.:110.0   3rd Qu.:1098.0   3rd Qu.:2832   3rd Qu.:4700  
##  Max.   :124.0   Max.   :1334.0   Max.   :3085   Max.   :5280

NipponSheetGlassCompany_TSE5202<- span=""> price4$x5202
PolaOrbisHoldings_TSE4927<- span=""> price4$x4927
YamahaMotor_TSE7272<- span=""> price4$x7272
TakedaPharmaceuticalCompany_TSE4502<- span=""> price4$x4502
par(mfcol=c(2,2))
plot(NipponSheetGlassCompany_TSE5202,type="l"
     ,main="NipponSheetGlassCompany_TSE5202")
plot(PolaOrbisHoldings_TSE4927,type="l"
     ,main="PolaOrbisHoldings_TSE4927")
plot(YamahaMotor_TSE7272,type="l"
     ,main="YamahaMotor_TSE7272")
plot(TakedaPharmaceuticalCompany_TSE4502,type="l"
     ,main="TakedaPharmaceuticalCompany_TSE4502")

 時系列の始点を基準として、価格収益率を求める

par(mfcol=c(2,2))
plot(NipponSheetGlassCompany_TSE5202/NipponSheetGlassCompany_TSE5202[1]
     ,type="l",main="NipponSheetGlassCompany_TSE5202")
plot(PolaOrbisHoldings_TSE4927/PolaOrbisHoldings_TSE4927[1]
     ,type="l",main="PolaOrbisHoldings_TSE4927")
plot(YamahaMotor_TSE7272/YamahaMotor_TSE7272[1]
     ,type="l",main="YamahaMotor_TSE7272")
plot(TakedaPharmaceuticalCompany_TSE4502/TakedaPharmaceuticalCompany_TSE4502[1]
     ,type="l",main="TakedaPharmaceuticalCompany_TSE4502")

 判明した点 板硝子は最高で2.2倍に株価が成長した

次に対数差収益を求める##

par(mfcol=c(2,2))
plot(diff(log(NipponSheetGlassCompany_TSE5202)*100)
     ,type="l",main="NipponSheetGlassCompany_TSE5202"
     ,xlab="time",ylab="NipponSheetGlassCompany_TSE5202")
plot(diff(log(PolaOrbisHoldings_TSE4927)*100)
     ,type="l",main="PolaOrbisHoldings_TSE4927"
     ,xlab="time",ylab="NipponSheetGlassCompany_TSE5202")
plot(diff(log(YamahaMotor_TSE7272)*100)
     ,type="l",main="YamahaMotor_TSE7272"
     ,xlab="time",ylab="NipponSheetGlassCompany_TSE5202")
plot(diff(log(TakedaPharmaceuticalCompany_TSE4502)*100)
     ,type="l",main="TakedaPharmaceuticalCompany_TSE4502"
     ,xlab="time",ylab="NipponSheetGlassCompany_TSE5202")

 結論 板硝子とYamahaMotor_TSE7272のボラは高い。一方、武田薬品のそれは低い

par(mfcol=c(2,2))
plot(diff(log(NipponSheetGlassCompany_TSE5202)*100)
     ,type="l",main="NipponSheetGlassCompany_TSE5202"
     ,xlab="time",ylab="NipponSheetGlassCompany_TSE5202"
     ,ylim=range(diff(log(NipponSheetGlassCompany_TSE5202))*100))
plot(diff(log(PolaOrbisHoldings_TSE4927)*100)
     ,type="l",main="PolaOrbisHoldings_TSE4927"
     ,xlab="time",ylab="PolaOrbisHoldings_TSE4927"
     ,ylim=range(diff(log(PolaOrbisHoldings_TSE4927))*100))
plot(diff(log(YamahaMotor_TSE7272)*100)
     ,type="l",main="YamahaMotor_TSE7272"
     ,xlab="time",ylab="YamahaMotor_TSE7272"
     ,ylim=range(diff(log(YamahaMotor_TSE7272))*100))
plot(diff(log(TakedaPharmaceuticalCompany_TSE4502)*100)
     ,type="l",main="TakedaPharmaceuticalCompany_TSE4502"
     ,xlab="time",ylab="TakedaPharmaceuticalCompany_TSE4502"
     ,ylim=range(diff(log(TakedaPharmaceuticalCompany_TSE4502))*100))

################################## ########時系列データ分布と要約########### ##4銘柄の平均収益率

mean(TakedaPharmaceuticalCompany_TSE4502)

## [1] 4199.38

mean(PolaOrbisHoldings_TSE4927)

## [1] 2633.157

mean(NipponSheetGlassCompany_TSE5202)

## [1] 92.39669

mean(YamahaMotor_TSE7272)

## [1] 968.8264

4銘柄のボラティリティ

sd(NipponSheetGlassCompany_TSE5202)

## [1] 20.12854

sd(PolaOrbisHoldings_TSE4927)

## [1] 209.8629

sd(YamahaMotor_TSE7272)

## [1] 187.3384

sd(TakedaPharmaceuticalCompany_TSE4502)

## [1] 571.4873

μ、σ、histgram

par(mfcol=c(2,2))
hist(NipponSheetGlassCompany_TSE5202,main="NipponSheetGlassCompany_TSE5202")
hist(PolaOrbisHoldings_TSE4927,main="PolaOrbisHoldings_TSE4927")
hist(YamahaMotor_TSE7272,main="YamahaMotor_TSE7272")
hist(TakedaPharmaceuticalCompany_TSE4502,main="TakedaPharmaceuticalCompany_TSE4502")

散布図行列

cor(YamahaMotor_TSE7272,TakedaPharmaceuticalCompany_TSE4502)

## [1] 0.9539355

plot(price4)

cor(price4)##相関係数行列

##           x5202     x7272     x4927     x4502
## x5202 1.0000000 0.8851551 0.7087943 0.8293775
## x7272 0.8851551 1.0000000 0.8705264 0.9539355
## x4927 0.7087943 0.8705264 1.0000000 0.9455436
## x4502 0.8293775 0.9539355 0.9455436 1.0000000

Shapiro-Wilk検定

shapiro.test(PolaOrbisHoldings_TSE4927)

## 
##  Shapiro-Wilk normality test
## 
## data:  PolaOrbisHoldings_TSE4927
## W = 0.85788, p-value = 2.071e-09

shapiro.test(TakedaPharmaceuticalCompany_TSE4502)

## 
##  Shapiro-Wilk normality test
## 
## data:  TakedaPharmaceuticalCompany_TSE4502
## W = 0.86407, p-value = 3.767e-09

shapiro.test(NipponSheetGlassCompany_TSE5202)

## 
##  Shapiro-Wilk normality test
## 
## data:  NipponSheetGlassCompany_TSE5202
## W = 0.91089, p-value = 6.758e-07

shapiro.test(YamahaMotor_TSE7272)

## 
##  Shapiro-Wilk normality test
## 
## data:  YamahaMotor_TSE7272
## W = 0.94524, p-value = 9.178e-05

　連の検定(runs test)

library(tseries)
yamaha=as.factor(YamahaMotor_TSE7272<mean(YamahaMotor_TSE7272))
runs.test(yamaha)

## 
##  Runs Test
## 
## data:  yamaha
## Standard Normal = -10.863, p-value < 2.2e-16
## alternative hypothesis: two.sided

Explore the time dependency for four stocks

par(mfcol=c(2,1))
plot(NipponSheetGlassCompany_TSE5202,type='l',main="NipponSheetGlassCompany_TSE5202")
plot(NipponSheetGlassCompany_TSE5202/NipponSheetGlassCompany_TSE5202[1]
     ,type="l",main="NipponSheetGlassCompany_TSE5202")
abline(h=0,lty=3)

par(mfcol=c(2,1))
plot(NipponSheetGlassCompany_TSE5202,type = 'l',main="PolaOrbisHoldings_TSE4927")
plot(PolaOrbisHoldings_TSE4927/PolaOrbisHoldings_TSE4927[1]
     ,type="l",main="PolaOrbisHoldings_TSE4927")
abline(h=0,lty=3)

par(mfcol=c(2,1))
plot(YamahaMotor_TSE7272,type = 'l',main="YamahaMotor_TSE7272")
plot(YamahaMotor_TSE7272/YamahaMotor_TSE7272[1]
     ,type="l",main="YamahaMotor_TSE7272")
abline(h=0,lty=3)

par(mfcol=c(2,1))
plot(TakedaPharmaceuticalCompany_TSE4502,type = 'l',main="TakedaPharmaceuticalCompany_TSE4502")
plot(TakedaPharmaceuticalCompany_TSE4502/TakedaPharmaceuticalCompany_TSE4502[1]
     ,type="l",main="TakedaPharmaceuticalCompany_TSE4502")
abline(h=0,lty=3)