ADEC7460 - Week 3 Discussion
Kayla Burt
11/9/2020
This dataset shows the employment rate of college graduates who have their Bachelor’s Degree and higher from ages 25 and over from January 1, 1992 to October 1, 2020.
library(fpp2)## Warning: package 'fpp2' was built under R version 4.0.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## -- 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(readxl)
employment<- read_excel("C:/Users/burtkb/Downloads/LNS12027662.xls", skip = 1)
e.ts = ts(employment[,2], start=c(1992,1), end=c(2020,10), frequency = 12)
sum(is.na(e.ts))## [1] 0There are 0 missing values.
e.ts2 = stl(e.ts, s.window="periodic")
dets = seasadj(e.ts2)
plot(dets)
ggseasonplot(dets)
There is an increasing trend, and there seems to be a bit of seasonality as it increases slightly over the summer and ends with a larger bump in October. This is the time when recent graduates are seeking employment.
#model1
fit1 = HoltWinters(dets)
f1 = forecast(fit1, 12)
print(summary(f1))##
## Forecast method: HoltWinters
##
## Model Information:
## Holt-Winters exponential smoothing with trend and additive seasonal component.
##
## Call:
## HoltWinters(x = dets)
##
## Smoothing parameters:
## alpha: 0.05610917
## beta : 0.6063179
## gamma: 0
##
## Coefficients:
## [,1]
## a 56876.27548
## b -943.31238
## s1 116.23702
## s2 115.13016
## s3 78.28245
## s4 26.94597
## s5 -29.52696
## s6 -117.13159
## s7 -203.04659
## s8 -161.78528
## s9 -123.83144
## s10 -194.91967
## s11 -255.78522
## s12 749.43116
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -88.85823 1769.131 346.7189 -0.3282525 0.9129443 0.2881122
## ACF1
## Training set 0.01499644
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2020 56049.20 53781.43 58316.97 52580.95 59517.45
## Dec 2020 55104.78 52827.82 57381.74 51622.47 58587.09
## Jan 2021 54124.62 51830.32 56418.92 50615.79 57633.45
## Feb 2021 53129.97 50807.80 55452.14 49578.52 56681.42
## Mar 2021 52130.19 49767.47 54492.90 48516.72 55743.65
## Apr 2021 51099.27 48681.50 53517.04 47401.62 54796.92
## May 2021 50070.04 47581.30 52558.79 46263.83 53876.25
## Jun 2021 49167.99 46591.34 51744.64 45227.34 53108.64
## Jul 2021 48262.63 45580.60 50944.67 44160.81 52364.45
## Aug 2021 47248.23 44443.18 50053.29 42958.27 51538.19
## Sep 2021 46244.05 43298.54 49189.57 41739.28 50748.83
## Oct 2021 46305.96 43202.99 49408.93 41560.38 51051.54
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2020 56049.20 53781.43 58316.97 52580.95 59517.45
## Dec 2020 55104.78 52827.82 57381.74 51622.47 58587.09
## Jan 2021 54124.62 51830.32 56418.92 50615.79 57633.45
## Feb 2021 53129.97 50807.80 55452.14 49578.52 56681.42
## Mar 2021 52130.19 49767.47 54492.90 48516.72 55743.65
## Apr 2021 51099.27 48681.50 53517.04 47401.62 54796.92
## May 2021 50070.04 47581.30 52558.79 46263.83 53876.25
## Jun 2021 49167.99 46591.34 51744.64 45227.34 53108.64
## Jul 2021 48262.63 45580.60 50944.67 44160.81 52364.45
## Aug 2021 47248.23 44443.18 50053.29 42958.27 51538.19
## Sep 2021 46244.05 43298.54 49189.57 41739.28 50748.83
## Oct 2021 46305.96 43202.99 49408.93 41560.38 51051.54#model2
fit2 = ets(dets)
f2 = forecast(fit2, 12)
print(summary(f2))##
## Forecast method: ETS(M,A,N)
##
## Model Information:
## ETS(M,A,N)
##
## Call:
## ets(y = dets)
##
## Smoothing parameters:
## alpha = 0.3372
## beta = 1e-04
##
## Initial states:
## l = 26868.7998
## b = 71.989
##
## sigma: 0.03
##
## AIC AICc BIC
## 6945.923 6946.099 6965.155
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -31.39286 1713.725 293.4481 -0.202378 0.8203071 0.2438459
## ACF1
## Training set 0.004504733
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2020 48406.67 46546.95 50266.38 45562.48 51250.86
## Dec 2020 48477.57 46512.25 50442.89 45471.87 51483.27
## Jan 2021 48548.47 46482.59 50614.36 45388.98 51707.97
## Feb 2021 48619.38 46457.27 50781.48 45312.72 51926.04
## Mar 2021 48690.28 46435.73 50944.83 45242.24 52138.32
## Apr 2021 48761.18 46417.52 51104.84 45176.87 52345.50
## May 2021 48832.08 46402.29 51261.88 45116.03 52548.14
## Jun 2021 48902.99 46389.71 51416.27 45059.26 52746.71
## Jul 2021 48973.89 46379.54 51568.24 45006.17 52941.61
## Aug 2021 49044.79 46371.55 51718.04 44956.42 53133.17
## Sep 2021 49115.70 46365.56 51865.83 44909.72 53321.67
## Oct 2021 49186.60 46361.40 52011.80 44865.83 53507.37
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Nov 2020 48406.67 46546.95 50266.38 45562.48 51250.86
## Dec 2020 48477.57 46512.25 50442.89 45471.87 51483.27
## Jan 2021 48548.47 46482.59 50614.36 45388.98 51707.97
## Feb 2021 48619.38 46457.27 50781.48 45312.72 51926.04
## Mar 2021 48690.28 46435.73 50944.83 45242.24 52138.32
## Apr 2021 48761.18 46417.52 51104.84 45176.87 52345.50
## May 2021 48832.08 46402.29 51261.88 45116.03 52548.14
## Jun 2021 48902.99 46389.71 51416.27 45059.26 52746.71
## Jul 2021 48973.89 46379.54 51568.24 45006.17 52941.61
## Aug 2021 49044.79 46371.55 51718.04 44956.42 53133.17
## Sep 2021 49115.70 46365.56 51865.83 44909.72 53321.67
## Oct 2021 49186.60 46361.40 52011.80 44865.83 53507.37#model comparison
par(mfrow=c(1,2))
plot(forecast(f1))
plot(forecast(f2))
accuracy(f1) #MAPE = ~0.913 = 99.087% accuracy## ME RMSE MAE MPE MAPE MASE
## Training set -88.85823 1769.131 346.7189 -0.3282525 0.9129443 0.2881122
## ACF1
## Training set 0.01499644accuracy(f2) #MAPE = ~0.820 = 99.180% accuracy## ME RMSE MAE MPE MAPE MASE
## Training set -31.39286 1713.725 293.4481 -0.202378 0.8203071 0.2438459
## ACF1
## Training set 0.004504733Based on the information above, we can see that model 2 (f2) is a slightly better model than the first (f1).