Find out correlation between Amazon and Ebay stock for past 5 years

Import the data and clean the data

AMZN <- read.csv("~/Documents/bc/forecasting/dis4/AMZN.csv")
EBAY <- read.csv("~/Documents/bc/forecasting/dis4/EBAY.csv")
library(fpp)
## Loading required package: forecast
## Warning: package 'forecast' was built under R version 3.4.4
## Loading required package: fma
## Loading required package: expsmooth
## Loading required package: lmtest
## Warning: package 'lmtest' was built under R version 3.4.4
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: tseries
## Warning: package 'tseries' was built under R version 3.4.4
library(vars)
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## The following objects are masked from 'package:fma':
## 
##     cement, housing, petrol
## Loading required package: strucchange
## Loading required package: sandwich
## Loading required package: urca
mydata=data.frame(AMZN$Adj.Close, EBAY$Adj.Close)
tsdata=ts(mydata, frequency = 252, start=c(2013,07,18))
plot(tsdata)

By looking at the graph, my guess that Amazon and Ebay are not very correlated

Build VAR Model

var1=VARselect(tsdata, lag.max=8, type="const")$selection
summary(var1)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     1.0     1.0     2.5     2.5     4.0     4.0
var2=VAR(tsdata, lag.max=8, type="const")
summary(var2)
## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: AMZN.Adj.Close, EBAY.Adj.Close 
## Deterministic variables: const 
## Sample size: 1255 
## Log Likelihood: -5756.885 
## Roots of the characteristic polynomial:
## 1.003 0.9888 0.4464 0.4464 0.377 0.3493 0.3493 0.2955
## Call:
## VAR(y = tsdata, type = "const", lag.max = 8)
## 
## 
## Estimation results for equation AMZN.Adj.Close: 
## =============================================== 
## AMZN.Adj.Close = AMZN.Adj.Close.l1 + EBAY.Adj.Close.l1 + AMZN.Adj.Close.l2 + EBAY.Adj.Close.l2 + AMZN.Adj.Close.l3 + EBAY.Adj.Close.l3 + AMZN.Adj.Close.l4 + EBAY.Adj.Close.l4 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)    
## AMZN.Adj.Close.l1  0.99240    0.02908  34.127  < 2e-16 ***
## EBAY.Adj.Close.l1  1.49744    0.80644   1.857  0.06357 .  
## AMZN.Adj.Close.l2  0.01740    0.04091   0.425  0.67061    
## EBAY.Adj.Close.l2 -2.45100    1.10879  -2.211  0.02725 *  
## AMZN.Adj.Close.l3 -0.10032    0.04093  -2.451  0.01440 *  
## EBAY.Adj.Close.l3  3.23680    1.10839   2.920  0.00356 ** 
## AMZN.Adj.Close.l4  0.09350    0.02927   3.195  0.00144 ** 
## EBAY.Adj.Close.l4 -2.28436    0.80911  -2.823  0.00483 ** 
## const             -0.72106    2.94737  -0.245  0.80677    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 12.84 on 1246 degrees of freedom
## Multiple R-Squared: 0.9989,  Adjusted R-squared: 0.9989 
## F-statistic: 1.397e+05 on 8 and 1246 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation EBAY.Adj.Close: 
## =============================================== 
## EBAY.Adj.Close = AMZN.Adj.Close.l1 + EBAY.Adj.Close.l1 + AMZN.Adj.Close.l2 + EBAY.Adj.Close.l2 + AMZN.Adj.Close.l3 + EBAY.Adj.Close.l3 + AMZN.Adj.Close.l4 + EBAY.Adj.Close.l4 + const 
## 
##                     Estimate Std. Error t value Pr(>|t|)    
## AMZN.Adj.Close.l1  0.0002828  0.0010525   0.269  0.78824    
## EBAY.Adj.Close.l1  0.9626417  0.0291891  32.980  < 2e-16 ***
## AMZN.Adj.Close.l2  0.0030517  0.0014807   2.061  0.03952 *  
## EBAY.Adj.Close.l2 -0.0527675  0.0401326  -1.315  0.18881    
## AMZN.Adj.Close.l3 -0.0039375  0.0014816  -2.658  0.00797 ** 
## EBAY.Adj.Close.l3  0.1255594  0.0401180   3.130  0.00179 ** 
## AMZN.Adj.Close.l4  0.0007729  0.0010594   0.730  0.46580    
## EBAY.Adj.Close.l4 -0.0476015  0.0292857  -1.625  0.10433    
## const              0.2391766  0.1066795   2.242  0.02514 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.4649 on 1246 degrees of freedom
## Multiple R-Squared: 0.9946,  Adjusted R-squared: 0.9946 
## F-statistic: 2.881e+04 on 8 and 1246 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                AMZN.Adj.Close EBAY.Adj.Close
## AMZN.Adj.Close        164.966         1.4507
## EBAY.Adj.Close          1.451         0.2161
## 
## Correlation matrix of residuals:
##                AMZN.Adj.Close EBAY.Adj.Close
## AMZN.Adj.Close          1.000          0.243
## EBAY.Adj.Close          0.243          1.000
serial.test(var2, lags.pt=8, type="PT.asymptotic")
## 
##  Portmanteau Test (asymptotic)
## 
## data:  Residuals of VAR object var2
## Chi-squared = 26.817, df = 16, p-value = 0.04357
fcast=forecast(var2,h=252)
plot(fcast)

The result proves my guess at first, they are weakly correlated at 0.243.

And for the forecast for the next year, both stcoks are going upwards slowly.