R Packages Utilized

library(readr)
library(ggplot2)
library(ggfortify)
library(vars)
library(forecast)
library(psych)

Importing 5 years of Monthly Adjusted Closing Data for two stocks

## I chose a monthly frequency for 1/1/2013 through 12/31/2018

## Walmart Stock (NYSE:WMT)
wmt <- read_csv("C:/Users/bryce_anderson/Desktop/Boston College/Predictive Analytics and Forecasting/Week 6 (PA&F)/WMT.csv")
## Source: https://finance.yahoo.com/quote/WMT/history?period1=1357016400&period2=1546232400&interval=1mo&filter=history&frequency=1mo


## Target Stock (NYSE:TGT)
tgt <- read_csv("C:/Users/bryce_anderson/Desktop/Boston College/Predictive Analytics and Forecasting/Week 6 (PA&F)/TGT.csv")
## Source: https://finance.yahoo.com/quote/TGT/history?period1=1357016400&period2=1546232400&interval=1mo&filter=history&frequency=1mo

Plotting and Inspecting both data sets

Walmart (NYSE:WMT)

## Walmart (NYSE:WMT)
wmtTS <- ts(wmt$close, frequency=12, start=c(2013,1)) ## Creating time series for close variable
autoplot(wmtTS) + xlab("Month") + ylab("Adjusted Monthly Close Price")

acf(wmtTS)

pacf(wmtTS)

checkresiduals(wmtTS)

Target (NYSE:TGT)

## Target (NYSE:TGT)
tgtTS <- ts(tgt$close, frequency=12, start=c(2013,1)) ## Creating time series for close variable
autoplot(tgtTS) + xlab("Month") + ylab("Adjusted Monthly Close Price")

acf(tgtTS)

pacf(tgtTS)

checkresiduals(tgtTS)

VAR Model of the time series

v1 <- VAR(cbind(wmtTS,tgtTS), p = 1, type = "both")
summary(v1)
## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: wmtTS, tgtTS 
## Deterministic variables: both 
## Sample size: 71 
## Log Likelihood: -386.377 
## Roots of the characteristic polynomial:
## 0.8855 0.8855
## Call:
## VAR(y = cbind(wmtTS, tgtTS), p = 1, type = "both")
## 
## 
## Estimation results for equation wmtTS: 
## ====================================== 
## wmtTS = wmtTS.l1 + tgtTS.l1 + const + trend 
## 
##          Estimate Std. Error t value Pr(>|t|)    
## wmtTS.l1  0.90127    0.05456  16.519   <2e-16 ***
## tgtTS.l1 -0.13622    0.05858  -2.325   0.0231 *  
## const    12.77208    4.29701   2.972   0.0041 ** 
## trend     0.07853    0.03217   2.441   0.0173 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.811 on 67 degrees of freedom
## Multiple R-Squared: 0.892,   Adjusted R-squared: 0.8872 
## F-statistic: 184.5 on 3 and 67 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation tgtTS: 
## ====================================== 
## tgtTS = wmtTS.l1 + tgtTS.l1 + const + trend 
## 
##          Estimate Std. Error t value Pr(>|t|)    
## wmtTS.l1 0.046776   0.056965   0.821    0.414    
## tgtTS.l1 0.862912   0.061162  14.109   <2e-16 ***
## const    4.977569   4.486441   1.109    0.271    
## trend    0.006157   0.033589   0.183    0.855    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.979 on 67 degrees of freedom
## Multiple R-Squared: 0.8197,  Adjusted R-squared: 0.8117 
## F-statistic: 101.6 on 3 and 67 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##       wmtTS tgtTS
## wmtTS 14.53  4.98
## tgtTS  4.98 15.84
## 
## Correlation matrix of residuals:
##        wmtTS  tgtTS
## wmtTS 1.0000 0.3284
## tgtTS 0.3284 1.0000
## Diagram of fit and residuals for both time series
plot(v1)