library(tidyverse)
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library(mosaic)
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library(ggformula)
library(readr)
library(fpp2)
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library(vars)
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##DISCUSSION WEEK 6
## READ IN Ford and GM DATA
uscars <- read_csv("E:/WOODS/ADECXXXX/uscars.csv")
## Parsed with column specification:
## cols(
## Date = col_character(),
## GM = col_double(),
## FORD = col_double()
## )
gmts <- ts(uscars$GM, start = c(2014, 1), frequency = 12)
fts <- ts(uscars$FORD, start = c(2014, 1), frequency = 12)
autoplot(gmts, series = "General Motors", lwd=2) + autolayer(fts, series = "Ford", lwd=2) + xlab("Year") + ylab("Monthly Adjusted Close") + theme_bw()
#How correlated are they anyways?
cor(uscars$GM, uscars$FORD)
## [1] -0.3600055
# Look at selection criteria for number of lags
VARselect(uscars[,2:3], lag.max=12, type="const")[["selection"]]
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 1 1 3
#SC says 1 lag; AIC says 3 ... so I checked 1, 2, and 3! All have high p-values, so none can be rejected. Therefore I will stick with 1 lag.
var1 <- VAR(uscars[,2:3], p=1, type="const")
serial.test(var1, lags.pt = 10, type = "PT.asymptotic")
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## Portmanteau Test (asymptotic)
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## data: Residuals of VAR object var1
## Chi-squared = 25.372, df = 36, p-value = 0.9069
var2 <- VAR(uscars[,2:3], p=2, type="const")
serial.test(var2, lags.pt = 10, type = "PT.asymptotic")
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## Portmanteau Test (asymptotic)
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## data: Residuals of VAR object var2
## Chi-squared = 24.568, df = 32, p-value = 0.8231
var3 <- VAR(uscars[,2:3], p=3, type="const")
serial.test(var3, lags.pt = 10, type = "PT.asymptotic")
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## Portmanteau Test (asymptotic)
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## data: Residuals of VAR object var3
## Chi-squared = 17.553, df = 28, p-value = 0.9368
# VAR model
varmodel <- VAR(uscars[,2:3], p=1, type="both")
summary(varmodel)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: GM, FORD
## Deterministic variables: both
## Sample size: 59
## Log Likelihood: -152.619
## Roots of the characteristic polynomial:
## 0.7436 0.4827
## Call:
## VAR(y = uscars[, 2:3], p = 1, type = "both")
##
##
## Estimation results for equation GM:
## ===================================
## GM = GM.l1 + FORD.l1 + const + trend
##
## Estimate Std. Error t value Pr(>|t|)
## GM.l1 0.76001 0.11173 6.802 7.95e-09 ***
## FORD.l1 -0.13699 0.50401 -0.272 0.787
## const 7.56931 5.01436 1.510 0.137
## trend 0.03965 0.04295 0.923 0.360
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 1.962 on 55 degrees of freedom
## Multiple R-Squared: 0.81, Adjusted R-squared: 0.7996
## F-statistic: 78.14 on 3 and 55 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation FORD:
## =====================================
## FORD = GM.l1 + FORD.l1 + const + trend
##
## Estimate Std. Error t value Pr(>|t|)
## GM.l1 0.03318 0.03229 1.028 0.308559
## FORD.l1 0.46630 0.14564 3.202 0.002272 **
## const 5.69538 1.44897 3.931 0.000239 ***
## trend -0.03663 0.01241 -2.952 0.004639 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.5669 on 55 degrees of freedom
## Multiple R-Squared: 0.7512, Adjusted R-squared: 0.7377
## F-statistic: 55.37 on 3 and 55 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## GM FORD
## GM 3.848 0.7350
## FORD 0.735 0.3213
##
## Correlation matrix of residuals:
## GM FORD
## GM 1.0000 0.6609
## FORD 0.6609 1.0000
plot(varmodel)
