week 6 discussion

Hanyue Kuang

for this discussion, I intend to look at the relationship between airline stock and oil stock. I choose jetblue and U.S.oil Fund to compare.

## Warning: package 'forecast' was built under R version 3.5.2

jblu <- read.csv("JBLU.csv")
uso <- read.csv("USO.csv")
stock <- data.frame(jblu$Adj.Close, uso$Adj.Close)
stock.ts <- ts(stock, start = c(2014,5), frequency=12)
jblu.ts <- ts(jblu$Adj.Close,start = c(2014,5), frequency=12)
uso.ts <- ts(uso$Adj.Close, start = c(2014,5), frequency=12)
autoplot(stock.ts)

par(mar=c(2.5,2.5,2.5,2.5))
acf(stock.ts)

autoplot(acf(diff(stock.ts)))

there is obvious autocorrelation existing and thus differencing is on demand.

stock.ts_diff <- diff(stock.ts)
VARselect(stock.ts_diff, lag.max = 8, type="const")$selection

## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      1      1      1      1

var <- VAR(stock.ts_diff, p=1)
summary(var)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: jblu.Adj.Close, uso.Adj.Close 
## Deterministic variables: const 
## Sample size: 58 
## Log Likelihood: -212.039 
## Roots of the characteristic polynomial:
## 0.3816 0.1815
## Call:
## VAR(y = stock.ts_diff, p = 1)
## 
## 
## Estimation results for equation jblu.Adj.Close: 
## =============================================== 
## jblu.Adj.Close = jblu.Adj.Close.l1 + uso.Adj.Close.l1 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)
## jblu.Adj.Close.l1 -0.19288    0.13457  -1.433    0.157
## uso.Adj.Close.l1  -0.18578    0.13003  -1.429    0.159
## const              0.06818    0.21383   0.319    0.751
## 
## 
## Residual standard error: 1.573 on 55 degrees of freedom
## Multiple R-Squared: 0.05813, Adjusted R-squared: 0.02388 
## F-statistic: 1.697 on 2 and 55 DF,  p-value: 0.1926 
## 
## 
## Estimation results for equation uso.Adj.Close: 
## ============================================== 
## uso.Adj.Close = jblu.Adj.Close.l1 + uso.Adj.Close.l1 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)   
## jblu.Adj.Close.l1  0.03517    0.13145   0.268   0.7900   
## uso.Adj.Close.l1   0.39301    0.12701   3.094   0.0031 **
## const             -0.26792    0.20886  -1.283   0.2050   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 1.536 on 55 degrees of freedom
## Multiple R-Squared: 0.1502,  Adjusted R-squared: 0.1193 
## F-statistic: 4.859 on 2 and 55 DF,  p-value: 0.01139 
## 
## 
## 
## Covariance matrix of residuals:
##                jblu.Adj.Close uso.Adj.Close
## jblu.Adj.Close          2.474        -0.361
## uso.Adj.Close          -0.361         2.361
## 
## Correlation matrix of residuals:
##                jblu.Adj.Close uso.Adj.Close
## jblu.Adj.Close         1.0000       -0.1494
## uso.Adj.Close         -0.1494        1.0000

autoplot(forecast(var, h=12))

seeing from the forecasting result, i think there is a relationship between this two. Also from the ts plot of the two, the data before 2015 deserves further analyzing.