Discussion 7
Tyler
4/25/2018
Load Data
library(forecast)## Warning: package 'forecast' was built under R version 3.4.4library(vars)## Loading required package: MASS## Loading required package: strucchange## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.4.3##
## 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: lmtestlibrary(readr)
BAC <- read_csv("~/Dropbox/Boston College/Predictive Analytics/Data/BAC.csv")## Parsed with column specification:
## cols(
## Date = col_date(format = ""),
## Open = col_character(),
## High = col_character(),
## Low = col_character(),
## Close = col_character(),
## `Adj Close` = col_character(),
## Volume = col_character()
## )JPM <- read_csv("~/Dropbox/Boston College/Predictive Analytics/Data/JPM.csv")## Parsed with column specification:
## cols(
## Date = col_date(format = ""),
## Open = col_character(),
## High = col_character(),
## Low = col_character(),
## Close = col_character(),
## `Adj Close` = col_character(),
## Volume = col_character()
## )stocks<-data.frame(BAC$`Adj Close`, JPM$`Adj Close`)
stocks<-stocks[-c(1),] #null first value
myts<-ts(stocks, start=c(2013, 5), end=c(2018,4), frequency=12)Evaluate Time Series
par(mfrow=c(1,1))
plot(myts)
VAR model
myvar<-VARselect(myts, lag.max = 8, type="const")
myvar## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 1 1 1 1
##
## $criteria
## 1 2 3 4 5
## AIC(n) 8.731625 8.869370 8.983451 9.099650 9.249192
## HQ(n) 8.817939 9.013228 9.184852 9.358594 9.565679
## SC(n) 8.956768 9.244609 9.508786 9.775081 10.074718
## FPE(n) 6197.374948 7119.282257 7996.343680 9015.403205 10531.894346
## 6 7 8
## AIC(n) 9.370237 9.496912 9.628016
## HQ(n) 9.744268 9.928485 10.117133
## SC(n) 10.345859 10.622629 10.903830
## FPE(n) 11990.723491 13775.058527 15960.002376var<-VAR(myts, p=1, lag.max=8, type="const")
summary(var)##
## VAR Estimation Results:
## =========================
## Endogenous variables: BAC..Adj.Close., JPM..Adj.Close.
## Deterministic variables: const
## Sample size: 59
## Log Likelihood: -413.951
## Roots of the characteristic polynomial:
## 0.9086 0.8694
## Call:
## VAR(y = myts, p = 1, type = "const", lag.max = 8)
##
##
## Estimation results for equation BAC..Adj.Close.:
## ================================================
## BAC..Adj.Close. = BAC..Adj.Close..l1 + JPM..Adj.Close..l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## BAC..Adj.Close..l1 0.882392 0.068060 12.965 <2e-16 ***
## JPM..Adj.Close..l1 -0.002789 0.066717 -0.042 0.9668
## const 4.427160 2.553584 1.734 0.0885 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 8.224 on 56 degrees of freedom
## Multiple R-Squared: 0.773, Adjusted R-squared: 0.7649
## F-statistic: 95.37 on 2 and 56 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation JPM..Adj.Close.:
## ================================================
## JPM..Adj.Close. = BAC..Adj.Close..l1 + JPM..Adj.Close..l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## BAC..Adj.Close..l1 -0.12216 0.07652 -1.597 0.1160
## JPM..Adj.Close..l1 0.89558 0.07501 11.940 <2e-16 ***
## const 6.68892 2.87098 2.330 0.0234 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 9.246 on 56 degrees of freedom
## Multiple R-Squared: 0.7281, Adjusted R-squared: 0.7184
## F-statistic: 74.98 on 2 and 56 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## BAC..Adj.Close. JPM..Adj.Close.
## BAC..Adj.Close. 67.64 32.51
## JPM..Adj.Close. 32.51 85.50
##
## Correlation matrix of residuals:
## BAC..Adj.Close. JPM..Adj.Close.
## BAC..Adj.Close. 1.0000 0.4275
## JPM..Adj.Close. 0.4275 1.0000serial.test(var, lags.pt=8, type="PT.asymptotic")##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object var
## Chi-squared = 5.573, df = 28, p-value = 1We see a correlation of 0.4275 of the residuals, meaning they are not significantly correlated.
Forecast
forecast<-forecast(var, h=12)
forecast## BAC..Adj.Close.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## May 2018 54.71235 44.17260 65.25210 38.593187 70.83151
## Jun 2018 52.69568 38.64867 66.74268 31.212638 74.17872
## Jul 2018 50.91713 34.65941 67.17485 26.053090 75.78117
## Aug 2018 49.34792 31.56005 67.13579 22.143716 76.55212
## Sep 2018 47.96280 29.06961 66.85598 19.068164 76.85743
## Oct 2018 46.73963 27.02834 66.45092 16.593813 76.88545
## Nov 2018 45.65900 25.33268 65.98531 14.572583 76.74541
## Dec 2018 44.70386 23.91022 65.49750 12.902730 76.50499
## Jan 2019 43.85925 22.70776 65.01074 11.510832 76.20767
## Feb 2019 43.11204 21.68492 64.53916 10.342085 75.88199
## Mar 2019 42.45068 20.81030 64.09105 9.354582 75.54678
## Apr 2019 41.86504 20.05906 63.67101 8.515681 75.21439
##
## JPM..Adj.Close.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## May 2018 3.307881 -8.541883 15.15764 -14.81477 21.43053
## Jun 2018 2.967500 -12.621472 18.55647 -20.87378 26.80878
## Jul 2018 2.909027 -14.981062 20.79912 -24.45150 30.26956
## Aug 2018 3.073935 -16.413654 22.56152 -26.72976 32.87763
## Sep 2018 3.413324 -17.265730 24.09238 -28.21256 35.03921
## Oct 2018 3.886487 -17.729067 25.50204 -29.17165 36.94462
## Nov 2018 4.459671 -17.922119 26.84146 -29.77032 38.68966
## Dec 2018 5.105018 -17.922833 28.13287 -30.11304 40.32308
## Jan 2019 5.799662 -17.784754 29.38408 -30.26959 41.86891
## Feb 2019 6.524954 -17.545903 30.59581 -30.28824 43.33815
## Mar 2019 7.265794 -17.234044 31.76563 -30.20348 44.73506
## Apr 2019 8.010071 -16.869944 32.89009 -30.04063 46.06077plot(forecast)
Looking at the forecasts, we confirm that JPM and BAC are not significantly correlated, which is very surprising.