道琼斯指数与成分股关系分析

1、获取数据

> library(quantmod)
> codedata<-list()
> codepool<-c("MMM","AXP","AAPL","BA","CAT","CVX","CSCO","KO","DD","XOM","GE","GS","HD","IBM","INTC","JNJ","JPM","MCD","MRK","MSFT","NKE","PFE","PG","TRV","UTX","UNH","VZ","WMT","V","DIS")
> number<-length(codepool)
> for(i in 1:number){
+ n<-codepool[i]
+ TESTdata<-get(getSymbols(n,src="yahoo",from=Sys.Date()-50,to=Sys.Date()))
+ codedata[[i]]<-as.data.frame(TESTdata[,4])
+ next}
> finaldata<-do.call(cbind,codedata)
> names(finaldata)<-codepool
> head(finaldata,3)
              MMM   AXP   AAPL     BA   CAT    CVX  CSCO    KO    DD   XOM    GE     GS     HD    IBM  INTC    JNJ   JPM    MCD   MRK  MSFT   NKE   PFE    PG    TRV
2017-01-23 178.51 75.97 120.08 157.84 94.46 115.39 30.27 41.43 72.78 84.97 29.75 232.67 138.07 171.03 36.77 113.91 83.71 121.38 61.81 62.96 53.24 31.46 86.96 118.04
2017-01-24 175.97 77.43 119.97 160.55 96.24 116.37 30.60 41.90 76.05 85.09 30.00 233.68 138.06 175.90 37.62 111.76 84.72 121.05 61.21 63.52 53.45 31.15 87.86 116.84
2017-01-25 176.73 76.89 121.88 167.36 98.15 117.24 30.70 42.12 76.67 85.34 30.37 237.25 137.48 178.29 37.80 112.80 86.03 121.79 61.08 63.68 53.86 31.29 87.16 117.67
              UTX    UNH    VZ   WMT     V    DIS
2017-01-23 110.34 159.07 52.41 66.65 82.15 107.12
2017-01-24 111.61 160.43 50.12 67.40 83.23 107.90
2017-01-25 110.96 161.24 49.77 66.89 83.90 108.04
> tail(finaldata,3)
              MMM   AXP   AAPL     BA   CAT    CVX  CSCO    KO    DD   XOM    GE     GS     HD    IBM  INTC    JNJ   JPM    MCD   MRK  MSFT   NKE   PFE    PG    TRV
2017-03-08 189.51 79.04 139.00 181.74 93.23 109.61 34.02 41.99 79.77 81.03 29.80 250.24 146.92 179.45 35.62 124.10 91.21 128.09 65.80 64.99 56.51 33.91 90.14 121.24
2017-03-09 189.90 79.30 138.68 180.57 91.39 110.04 34.07 42.03 80.48 81.67 29.66 250.18 146.62 177.18 35.82 125.95 91.57 128.14 65.89 64.73 56.36 34.05 90.34 121.90
2017-03-10 191.21 79.38 139.14 178.70 92.31 110.61 34.26 42.29 80.86 81.61 30.28 248.38 146.85 177.83 35.91 126.21 91.28 127.98 65.60 64.93 56.43 34.11 91.07 122.83
              UTX    UNH    VZ   WMT     V    DIS
2017-03-08 111.75 167.91 49.16 69.80 88.96 110.84
2017-03-09 111.93 168.01 49.28 69.86 89.11 111.03
2017-03-10 112.14 169.98 49.35 70.10 89.73 110.92

道琼斯指数共有30只成分股，取各个成分股最近50天的收盘价。

2、主成分分析

> p<-princomp(finaldata[,1:30])
> summary(p)
Importance of components:
                           Comp.1     Comp.2     Comp.3     Comp.4     Comp.5      Comp.6      Comp.7      Comp.8      Comp.9     Comp.10     Comp.11     Comp.12
Standard deviation     16.1041328 4.22688825 3.50222384 2.20689405 2.01370950 1.459120153 1.298793653 0.991546988 0.858445383 0.752024098 0.679270196 0.579182056
Proportion of Variance  0.8458697 0.05827339 0.04000521 0.01588517 0.01322581 0.006944019 0.005501855 0.003206678 0.002403555 0.001844558 0.001504922 0.001094105
Cumulative Proportion   0.8458697 0.90414310 0.94414831 0.96003348 0.97325929 0.980203314 0.985705168 0.988911847 0.991315402 0.993159960 0.994664882 0.995758987

主成分分析法生成了30个新变量，前面3个变量能够解释到原数据集94.41%(0.8458697+0.05827339+0.04000521)的方差，所以咱们能够用这3个新的变量代替原来30个初始变量。

> stockdata<-as.data.frame(as.matrix(finaldata[,1:30])%*%as.matrix(p$loadings[,1:3]))
> head(stockdata)
              Comp.1    Comp.2   Comp.3
2017-01-23 -497.0058 -3.717498 174.8456
2017-01-24 -498.6973 -5.271716 178.5616
2017-01-25 -505.3037 -4.955875 181.6700
2017-01-26 -507.5417 -4.710687 182.2582
2017-01-27 -506.5475 -3.575603 180.2852
2017-01-30 -502.8693 -3.291562 176.4937

3、回归分析

一、获取道琼斯指数最近50天数据，合并数据框

> res<-get(getSymbols("DJIA",src="yahoo",from=Sys.Date()-50,to=Sys.Date()))
> US30<-as.data.frame(res[,4])
> mydata<-cbind(stockdata,US30)
> names(mydata)<-c("X1","X2","X3","US30")
> head(mydata)
                  X1        X2       X3     US30
2017-01-23 -497.0058 -3.717498 174.8456 19799.85
2017-01-24 -498.6973 -5.271716 178.5616 19912.71
2017-01-25 -505.3037 -4.955875 181.6700 20068.51
2017-01-26 -507.5417 -4.710687 182.2582 20100.91
2017-01-27 -506.5475 -3.575603 180.2852 20093.78
2017-01-30 -502.8693 -3.291562 176.4937 19971.13

二、构造多元线性回归模型

> model<-lm(US30~X1+X2+X3,mydata)
> summary(model)

Call:
lm(formula = US30 ~ X1 + X2 + X3, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-50.267  -7.866  -1.937  10.018  39.555 

Coefficients:
             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 5395.8202   218.4604   24.699  < 2e-16 ***
X1           -25.7840     0.2282 -113.006  < 2e-16 ***
X2             0.4522     0.8693    0.520    0.607    
X3             9.1254     1.0492    8.698 1.06e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 21.43 on 30 degrees of freedom
Multiple R-squared:  0.9977,    Adjusted R-squared:  0.9974 
F-statistic:  4282 on 3 and 30 DF,  p-value: < 2.2e-16
> model

Call:
lm(formula = US30 ~ X1 + X2 + X3, data = mydata)

Coefficients:
(Intercept)           X1           X2           X3  
  5395.8202     -25.7840       0.4522       9.1254

检验显示X2与US30不显著,剔除X2。所以线性回归方程为：

> US30 = 5395.8202 + -25.7840*X1 + 9.1254*X3