ADEC7460 - Week 5 Discussion

A Closer Look at the Higher-Ed Work Force Since 2000.

Estimated number of workers employed by institutions of higher education.https://www.chronicle.com/article/colleges-have-shed-a-tenth-of-their-employees-since-the-pandemic-began?utm_source=Iterable&utm_medium=email&utm_campaign=campaign_1706047_nl_Academe-Today_date_20201111&cid=at&source=&sourceId=

library(quantmod)

## Warning: package 'quantmod' was built under R version 4.0.3

## Loading required package: xts

## Warning: package 'xts' was built under R version 4.0.2

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 4.0.2

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## Loading required package: TTR

## Warning: package 'TTR' was built under R version 4.0.2

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## Version 0.4-0 included new data defaults. See ?getSymbols.

library(fpp2)

## Warning: package 'fpp2' was built under R version 4.0.3

## -- Attaching packages ------------------------------------ fpp2 2.4 --

## v ggplot2   3.3.0     v fma       2.4  
## v forecast  8.12      v expsmooth 2.3

## Warning: package 'forecast' was built under R version 4.0.2

## Warning: package 'fma' was built under R version 4.0.3

## Warning: package 'expsmooth' was built under R version 4.0.3

## 

library(knitr)
library(rugarch)

## Warning: package 'rugarch' was built under R version 4.0.3

## Loading required package: parallel

## 
## Attaching package: 'rugarch'

## The following object is masked from 'package:stats':
## 
##     sigma

library(fGarch)

## Warning: package 'fGarch' was built under R version 4.0.3

## Loading required package: timeDate

## Loading required package: timeSeries

## Warning: package 'timeSeries' was built under R version 4.0.3

## 
## Attaching package: 'timeSeries'

## The following object is masked from 'package:zoo':
## 
##     time<-

## Loading required package: fBasics

## Warning: package 'fBasics' was built under R version 4.0.3

## 
## Attaching package: 'fBasics'

## The following object is masked from 'package:TTR':
## 
##     volatility

library(tseries)

## Warning: package 'tseries' was built under R version 4.0.2

library(bayesGARCH)

## Warning: package 'bayesGARCH' was built under R version 4.0.3

highered <- read.csv("C:/Users/burtkb/Downloads/data-3qXvL.csv", skip = 1)
he.ts = ts(highered[,2], start=c(2000,1), end=c(2020,10), frequency = 12)
autoplot(he.ts)

he.train = window(he.ts, start=c(2000,1),  end=c(2019,12),frequency=12)
he.test = window(he.ts,start=c(2020,1), end=c(2020,10),frequency=12)

mean(he.train, na.rm=TRUE)

## [1] 4226148

mean(he.test)

## [1] 4423500

he.bc =BoxCox(he.train, lambda=BoxCox.lambda(he.train))
he.ts2 = stl(he.bc, s.window="periodic")
d.hets = seasadj(he.ts2)
autoplot(d.hets)

Models

#model3 - garch
fit3 = garch(d.hets)

## 
##  ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 
## 
## 
##      I     INITIAL X(I)        D(I)
## 
##      1     1.447178e+24     1.000e+00
##      2     5.000000e-02     1.000e+00
##      3     5.000000e-02     1.000e+00
## 
##     IT   NF      F         RELDF    PRELDF    RELDX   STPPAR   D*STEP   NPRELDF
##      0    1  8.468e+03
##      1    2  7.247e+03  1.44e-01  2.66e+00  3.4e-25  2.3e+04  1.0e+00  3.00e+04
## 
##  ***** FALSE CONVERGENCE *****
## 
##  FUNCTION     7.247436e+03   RELDX        3.446e-25
##  FUNC. EVALS       2         GRAD. EVALS       2
##  PRELDF       2.663e+00      NPRELDF      3.002e+04
## 
##      I      FINAL X(I)        D(I)          G(I)
## 
##      1    1.447178e+24     1.000e+00     2.603e-25
##      2    1.047343e+00     1.000e+00     1.942e+01
##      3    1.228444e-01     1.000e+00     2.360e+01

## Warning in garch(d.hets): singular information

## Warning in sqrt(pred$e): NaNs produced

fit3

## 
## Call:
## garch(x = d.hets)
## 
## Coefficient(s):
##        a0         a1         b1  
## 1.447e+24  1.047e+00  1.228e-01

plot(fit3)

summary(fit3)

## 
## Call:
## garch(x = d.hets)
## 
## Model:
## GARCH(1,1)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## 0.9005 0.9079 0.9095 0.9106 0.9769 
## 
## Coefficient(s):
##     Estimate  Std. Error  t value Pr(>|t|)
## a0 1.447e+24          NA       NA       NA
## a1 1.047e+00          NA       NA       NA
## b1 1.228e-01          NA       NA       NA
## 
## Diagnostic Tests:
##  Jarque Bera Test
## 
## data:  Residuals
## X-squared = 112374, df = 2, p-value < 2.2e-16
## 
## 
##  Box-Ljung test
## 
## data:  Squared.Residuals
## X-squared = 8.6409, df = 1, p-value = 0.003287