# The two stock I choose are Facebook and Tesla. They are the world's most recognizable brands. It is believed that these two stock share some similar pattern.
library(fpp2)
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 3.6.2
## Loading required package: forecast
## Warning: package 'forecast' was built under R version 3.6.2
## Registered S3 method overwritten by 'xts':
## method from
## as.zoo.xts zoo
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## Loading required package: fma
## Loading required package: expsmooth
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: 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
FB <- read.csv('/Users/jiahaolin/Downloads/Forecasting/week 6/FB.csv')
TSLA <- read.csv('/Users/jiahaolin/Downloads/Forecasting/week 6/TSLA.csv')
ts(FB['Adj.Close']) %>% autoplot(series='FB')+
ts(TSLA['Adj.Close']) %>% autolayer(series='TSLA')
# Although two stocks differ from each other in the magnitudes, they fluctuate in the same direction.
stock <- cbind(FB['Adj.Close'],TSLA['Adj.Close']) #Here, I build a data containing both stock prices.
names(stock) <- c('FB','TSLA')
stock.var1 <- VAR(stock, type='const', lag.max=1, ic='AIC') # First, let's try lag 1.
stock.var1
##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation FB:
## =======================================
## Call:
## FB = FB.l1 + TSLA.l1 + const
##
## FB.l1 TSLA.l1 const
## 0.9947690854 0.0006786073 0.7171436931
##
##
## Estimated coefficients for equation TSLA:
## =========================================
## Call:
## TSLA = FB.l1 + TSLA.l1 + const
##
## FB.l1 TSLA.l1 const
## 0.022113 1.005170 -4.283316
ts(FB['Adj.Close']) %>% autoplot(series='FB')+
ts(fitted(stock.var1)[,1]) %>% autolayer(series='FB.fit')
# The fitted value overlaps the actual one.
# We can check the result by using normal linear regression:
FB.lm <- lm(FB[2:nrow(stock)]~FB[1:(nrow(stock)-1)]+TSLA[1:(nrow(stock)-1)], data=stock)
TSLA.lm <- lm(TSLA[2:nrow(stock)]~TSLA[1:(nrow(stock)-1)]+FB[1:(nrow(stock)-1)], data=stock)
FB.lm
##
## Call:
## lm(formula = FB[2:nrow(stock)] ~ FB[1:(nrow(stock) - 1)] + TSLA[1:(nrow(stock) -
## 1)], data = stock)
##
## Coefficients:
## (Intercept) FB[1:(nrow(stock) - 1)]
## 0.7171437 0.9947691
## TSLA[1:(nrow(stock) - 1)]
## 0.0006786
TSLA.lm # The results are similar with what we get from VAR model. It shows that both FB and TSLA stock price in lag 1 are positively affect the current FB and TSLA stock price.
##
## Call:
## lm(formula = TSLA[2:nrow(stock)] ~ TSLA[1:(nrow(stock) - 1)] +
## FB[1:(nrow(stock) - 1)], data = stock)
##
## Coefficients:
## (Intercept) TSLA[1:(nrow(stock) - 1)]
## -4.28332 1.00517
## FB[1:(nrow(stock) - 1)]
## 0.02211
# Now, let's try lag 10:
stock.var10 <- VAR(stock, type='const', lag.max=10, ic='AIC')
stock.var10
##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation FB:
## =======================================
## Call:
## FB = FB.l1 + TSLA.l1 + FB.l2 + TSLA.l2 + FB.l3 + TSLA.l3 + FB.l4 + TSLA.l4 + FB.l5 + TSLA.l5 + FB.l6 + TSLA.l6 + FB.l7 + TSLA.l7 + FB.l8 + TSLA.l8 + FB.l9 + TSLA.l9 + FB.l10 + TSLA.l10 + const
##
## FB.l1 TSLA.l1 FB.l2 TSLA.l2 FB.l3
## 0.9482240030 -0.0128707513 0.0338896007 0.0307309716 -0.0219028839
## TSLA.l3 FB.l4 TSLA.l4 FB.l5 TSLA.l5
## -0.0126474440 0.0251808795 0.0017821483 -0.0190418016 -0.0071458097
## FB.l6 TSLA.l6 FB.l7 TSLA.l7 FB.l8
## -0.0114036876 -0.0054059346 0.0878136282 0.0013571989 -0.1122692777
## TSLA.l8 FB.l9 TSLA.l9 FB.l10 TSLA.l10
## -0.0007821859 0.0918184608 0.0132098672 -0.0268071865 -0.0076371510
## const
## 0.6492238172
##
##
## Estimated coefficients for equation TSLA:
## =========================================
## Call:
## TSLA = FB.l1 + TSLA.l1 + FB.l2 + TSLA.l2 + FB.l3 + TSLA.l3 + FB.l4 + TSLA.l4 + FB.l5 + TSLA.l5 + FB.l6 + TSLA.l6 + FB.l7 + TSLA.l7 + FB.l8 + TSLA.l8 + FB.l9 + TSLA.l9 + FB.l10 + TSLA.l10 + const
##
## FB.l1 TSLA.l1 FB.l2 TSLA.l2 FB.l3
## 0.171938837 0.988659082 -0.137407121 0.043093454 -0.022173757
## TSLA.l3 FB.l4 TSLA.l4 FB.l5 TSLA.l5
## 0.097376761 0.449331720 -0.261108680 -1.147922661 0.248959947
## FB.l6 TSLA.l6 FB.l7 TSLA.l7 FB.l8
## 0.460031851 -0.114685424 0.658925016 0.005859767 -0.449950884
## TSLA.l8 FB.l9 TSLA.l9 FB.l10 TSLA.l10
## 0.004285374 -0.066824521 -0.075955484 0.104231917 0.068669270
## const
## -4.004057727
ts(FB['Adj.Close']) %>% autoplot(series='FB')+
ts(fitted(stock.var10)[,1]) %>% autolayer(series='FB.fit')
# The fiited value leads the actual one.