setwd("~/desktop/ADEC7460.02 Spring 2019 Predictive Analytics/Dataset")
sina=read.csv("SINA.csv")
bidu=read.csv("BIDU.csv")

library(forecast)
library(ggplot2)
library(vars)
## Loading required package: MASS
## Loading required package: strucchange
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: urca
## Loading required package: lmtest
library(zoo)
stocks<-data.frame(sina$Adj.Close, bidu$Adj.Close)
mod<-stocks[-1,]
mod$sina.Adj.Close<-as.numeric(as.character(mod$sina.Adj.Close))
mod$bidu.Adj.Close<-as.numeric(as.character(mod$bidu.Adj.Close))
stocks.ts<-ts(mod, frequency=12,start = c(2014,5))
autoplot(stocks.ts)

The graph shows that the similiar trend of two stocks after 2016. And Baidu stock price is much higher than Sina’s.

stock.var1<-VAR(stocks.ts, p=1, type="both")
summary(stock.var1)
## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: sina.Adj.Close, bidu.Adj.Close 
## Deterministic variables: both 
## Sample size: 59 
## Log Likelihood: -442.806 
## Roots of the characteristic polynomial:
## 0.8734 0.8734
## Call:
## VAR(y = stocks.ts, p = 1, type = "both")
## 
## 
## Estimation results for equation sina.Adj.Close: 
## =============================================== 
## sina.Adj.Close = sina.Adj.Close.l1 + bidu.Adj.Close.l1 + const + trend 
## 
##                   Estimate Std. Error t value Pr(>|t|)    
## sina.Adj.Close.l1  0.98964    0.06649  14.885   <2e-16 ***
## bidu.Adj.Close.l1 -0.06931    0.03692  -1.877   0.0658 .  
## const             15.24423    6.55057   2.327   0.0237 *  
## trend             -0.01437    0.08252  -0.174   0.8624    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 7.522 on 55 degrees of freedom
## Multiple R-Squared: 0.9034,  Adjusted R-squared: 0.8981 
## F-statistic: 171.5 on 3 and 55 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation bidu.Adj.Close: 
## =============================================== 
## bidu.Adj.Close = sina.Adj.Close.l1 + bidu.Adj.Close.l1 + const + trend 
## 
##                   Estimate Std. Error t value Pr(>|t|)    
## sina.Adj.Close.l1  0.35813    0.14547   2.462  0.01698 *  
## bidu.Adj.Close.l1  0.74564    0.08079   9.230 9.09e-13 ***
## const             39.47333   14.33290   2.754  0.00796 ** 
## trend             -0.39386    0.18055  -2.181  0.03344 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 16.46 on 55 degrees of freedom
## Multiple R-Squared: 0.7373,  Adjusted R-squared: 0.7229 
## F-statistic: 51.45 on 3 and 55 DF,  p-value: 5.633e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                sina.Adj.Close bidu.Adj.Close
## sina.Adj.Close          56.58          47.93
## bidu.Adj.Close          47.93         270.89
## 
## Correlation matrix of residuals:
##                sina.Adj.Close bidu.Adj.Close
## sina.Adj.Close         1.0000         0.3872
## bidu.Adj.Close         0.3872         1.0000
acf(residuals(stock.var1)[,1])

acf(residuals(stock.var1)[,2])

autoplot(forecast(stock.var1,h=12))

stock.var2<-VAR(stocks.ts,p=1, type="const")
summary(stock.var2)
## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: sina.Adj.Close, bidu.Adj.Close 
## Deterministic variables: const 
## Sample size: 59 
## Log Likelihood: -445.514 
## Roots of the characteristic polynomial:
## 0.8882 0.8882
## Call:
## VAR(y = stocks.ts, p = 1, type = "const")
## 
## 
## Estimation results for equation sina.Adj.Close: 
## =============================================== 
## sina.Adj.Close = sina.Adj.Close.l1 + bidu.Adj.Close.l1 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)    
## sina.Adj.Close.l1  0.98141    0.04635  21.176   <2e-16 ***
## bidu.Adj.Close.l1 -0.06752    0.03516  -1.920   0.0599 .  
## const             14.98131    6.31875   2.371   0.0212 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 7.457 on 56 degrees of freedom
## Multiple R-Squared: 0.9034,  Adjusted R-squared: 0.8999 
## F-statistic: 261.7 on 2 and 56 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation bidu.Adj.Close: 
## =============================================== 
## bidu.Adj.Close = sina.Adj.Close.l1 + bidu.Adj.Close.l1 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)    
## sina.Adj.Close.l1  0.13250    0.10567   1.254   0.2151    
## bidu.Adj.Close.l1  0.79467    0.08016   9.913 6.26e-14 ***
## const             32.26621   14.40741   2.240   0.0291 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 17 on 56 degrees of freedom
## Multiple R-Squared: 0.7145,  Adjusted R-squared: 0.7043 
## F-statistic: 70.09 on 2 and 56 DF,  p-value: 5.69e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                sina.Adj.Close bidu.Adj.Close
## sina.Adj.Close          55.60          47.92
## bidu.Adj.Close          47.92         289.07
## 
## Correlation matrix of residuals:
##                sina.Adj.Close bidu.Adj.Close
## sina.Adj.Close          1.000          0.378
## bidu.Adj.Close          0.378          1.000
acf(residuals(stock.var2)[,1])

acf(residuals(stock.var2)[,2])

autoplot(forecast(stock.var2,h=12))

From the analysis above,Sina and Baidu are internet giants in China and I deemed that there are some correlations between these two stocks.