discussion 6
Nelson White
12/06/2020
Libraries
library(vars)## Loading required package: MASS## Warning: package 'MASS' was built under R version 3.6.2## Loading required package: strucchange## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.6.2##
## 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(knitr)
library(tidyverse)## ── Attaching packages ──────────────────────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.2 ✓ purrr 0.3.4
## ✓ tibble 3.0.1 ✓ dplyr 0.8.5
## ✓ tidyr 1.0.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.4.0## Warning: package 'ggplot2' was built under R version 3.6.2## Warning: package 'tibble' was built under R version 3.6.2## Warning: package 'purrr' was built under R version 3.6.2## ── Conflicts ─────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## x stringr::boundary() masks strucchange::boundary()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x dplyr::select() masks MASS::select()library(quantmod)## Loading required package: xts## Registered S3 method overwritten by 'xts':
## method from
## as.zoo.xts zoo##
## Attaching package: 'xts'## The following objects are masked from 'package:dplyr':
##
## first, last## Loading required package: TTR## Warning: package 'TTR' was built under R version 3.6.2## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Version 0.4-0 included new data defaults. See ?getSymbols.library(forecast)## Warning: package 'forecast' was built under R version 3.6.2Load Data & Features
I chose Hilton (HLT) and Delta (DAL) as the two stocks to compare. I am not sure about the historical data, but I suspect that after the Covid-induced market crash in March 2020, there will be a clear pattern.
delta = read.csv("/Users/nelsonwhite/Documents/ms applied economics/Predictive Analytics:Forecasting/week 6 discussion/DAL.csv")
hilton = read.csv("/Users/nelsonwhite/Documents/ms applied economics/Predictive Analytics:Forecasting/week 6 discussion/HLT.csv")delta.ts = ts(delta[,6], frequency=12)
hilton.ts = ts(hilton[,6], frequency=12)
pricediff = (delta.ts-hilton.ts)
prices = cbind(delta.ts,hilton.ts)autoplot(prices)
There is apparent seasonality in both stocks. We can see at month = 50, there is a significant dip in prices for both.
autoplot(pricediff)
However the price difference has a clear downward trend and it’s defiend as delta-hilton, meaning that even though both stocks becan at similar values in 2015, Hilton has become more valuable than Delta over time.
acf(prices)
VARselect(prices)## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 1 1 3
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 6.375205 6.415769 6.362507 6.468346 6.598901 6.684348
## HQ(n) 6.462578 6.561391 6.566378 6.730466 6.919269 7.062965
## SC(n) 6.604648 6.798174 6.897874 7.156675 7.440191 7.678600
## FPE(n) 587.275277 612.231738 581.848319 649.548198 745.105285 819.571786
## 7 8 9 10
## AIC(n) 6.813025 6.811270 6.920761 6.994963
## HQ(n) 7.249891 7.306385 7.474124 7.606574
## SC(n) 7.960239 8.111446 8.373898 8.601062
## FPE(n) 944.923327 960.679250 1097.729913 1218.932336VARselect recommends 3 and 1 equally.
prices.var1 = VAR(prices, lag.max = 3)
prices.var1##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation delta.ts:
## =============================================
## Call:
## delta.ts = delta.ts.l1 + hilton.ts.l1 + const
##
## delta.ts.l1 hilton.ts.l1 const
## 0.888499615 -0.002361582 5.104590111
##
##
## Estimated coefficients for equation hilton.ts:
## ==============================================
## Call:
## hilton.ts = delta.ts.l1 + hilton.ts.l1 + const
##
## delta.ts.l1 hilton.ts.l1 const
## -0.1265878 0.9732574 8.7209150forecast(prices.var1)## delta.ts
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 6 39.32141 33.55557 45.08725 30.50332 48.13950
## Feb 6 39.79120 32.08642 47.49598 28.00775 51.57464
## Mar 6 40.20646 31.26834 49.14459 26.53678 53.87614
## Apr 6 40.57348 30.77414 50.37282 25.58668 55.56028
## May 6 40.89781 30.47100 51.32461 24.95139 56.84423
## Jun 6 41.18436 30.28924 52.07948 24.52172 57.84700
## Jul 6 41.43749 30.18743 52.68755 24.23201 58.64297
## Aug 6 41.66105 30.13914 53.18296 24.03981 59.28229
## Sep 6 41.85845 30.12674 53.59015 23.91635 59.80054
## Oct 6 42.03270 30.13816 53.92724 23.84157 60.22383
##
## hilton.ts
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 6 106.0513 97.85065 114.2519 93.50950 118.5930
## Feb 6 106.9585 95.81970 118.0973 89.92318 123.9938
## Mar 6 107.7820 94.63423 120.9297 87.67423 127.8897
## Apr 6 108.5309 93.85273 123.2090 86.08259 130.9792
## May 6 109.2133 93.30056 125.1261 84.87686 133.5498
## Jun 6 109.8364 92.88893 126.7839 83.91748 135.7554
## Jul 6 110.4066 92.56707 128.2461 83.12340 137.6898
## Aug 6 110.9295 92.30400 129.5549 82.44427 139.4147
## Sep 6 111.4101 92.08013 130.7400 81.84748 140.9727
## Oct 6 111.8528 91.88285 131.8228 81.31138 142.3943autoplot(forecast(prices.var1))
prices.var2 = VAR(prices, lag.max=1)
prices.var2##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation delta.ts:
## =============================================
## Call:
## delta.ts = delta.ts.l1 + hilton.ts.l1 + const
##
## delta.ts.l1 hilton.ts.l1 const
## 0.888499615 -0.002361582 5.104590111
##
##
## Estimated coefficients for equation hilton.ts:
## ==============================================
## Call:
## hilton.ts = delta.ts.l1 + hilton.ts.l1 + const
##
## delta.ts.l1 hilton.ts.l1 const
## -0.1265878 0.9732574 8.7209150forecast(prices.var2)## delta.ts
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 6 39.32141 33.55557 45.08725 30.50332 48.13950
## Feb 6 39.79120 32.08642 47.49598 28.00775 51.57464
## Mar 6 40.20646 31.26834 49.14459 26.53678 53.87614
## Apr 6 40.57348 30.77414 50.37282 25.58668 55.56028
## May 6 40.89781 30.47100 51.32461 24.95139 56.84423
## Jun 6 41.18436 30.28924 52.07948 24.52172 57.84700
## Jul 6 41.43749 30.18743 52.68755 24.23201 58.64297
## Aug 6 41.66105 30.13914 53.18296 24.03981 59.28229
## Sep 6 41.85845 30.12674 53.59015 23.91635 59.80054
## Oct 6 42.03270 30.13816 53.92724 23.84157 60.22383
##
## hilton.ts
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 6 106.0513 97.85065 114.2519 93.50950 118.5930
## Feb 6 106.9585 95.81970 118.0973 89.92318 123.9938
## Mar 6 107.7820 94.63423 120.9297 87.67423 127.8897
## Apr 6 108.5309 93.85273 123.2090 86.08259 130.9792
## May 6 109.2133 93.30056 125.1261 84.87686 133.5498
## Jun 6 109.8364 92.88893 126.7839 83.91748 135.7554
## Jul 6 110.4066 92.56707 128.2461 83.12340 137.6898
## Aug 6 110.9295 92.30400 129.5549 82.44427 139.4147
## Sep 6 111.4101 92.08013 130.7400 81.84748 140.9727
## Oct 6 111.8528 91.88285 131.8228 81.31138 142.3943autoplot(forecast(prices.var2))