h3
James Lunga
12/13/2021
library(rmarkdown)## Warning: package 'rmarkdown' was built under R version 4.0.5library(forecast)## Warning: package 'forecast' was built under R version 4.0.5## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(tseries)## Warning: package 'tseries' was built under R version 4.0.5library(timeSeries)## Warning: package 'timeSeries' was built under R version 4.0.5## Loading required package: timeDate## Warning: package 'timeDate' was built under R version 4.0.5library(xts)## Warning: package 'xts' was built under R version 4.0.5## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.0.5##
## Attaching package: 'zoo'## The following object is masked from 'package:timeSeries':
##
## time<-## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(quantmod)## Warning: package 'quantmod' was built under R version 4.0.5## Loading required package: TTR## Warning: package 'TTR' was built under R version 4.0.5library(readr)## Warning: package 'readr' was built under R version 4.0.5library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.0.5mydata <- read.csv("~/College Documents/Boston College/unemployment.csv")
str(mydata)## 'data.frame': 382 obs. of 2 variables:
## $ DATE: chr "1990-01" "1990-02" "1990-03" "1990-04" ...
## $ u : num 10 10.1 10.1 10.1 10.3 ...mydata=ts(mydata$u, frequency=12, start=c(1990,1))
plot(mydata)
train.ts<-window(mydata, end=c(2019,12))
test.ts<-window(mydata,start=c(2017,1))
plot(decompose(train.ts))
acf(train.ts)
pacf(train.ts)
fit.nn<-nnetar(train.ts)
fit.ets<-ets(train.ts)
fit.aa<-auto.arima(train.ts)
fit.nn## Series: train.ts
## Model: NNAR(25,1,13)[12]
## Call: nnetar(y = train.ts)
##
## Average of 20 networks, each of which is
## a 25-13-1 network with 352 weights
## options were - linear output units
##
## sigma^2 estimated as 0.0007581fit.ets## ETS(M,N,N)
##
## Call:
## ets(y = train.ts)
##
## Smoothing parameters:
## alpha = 0.8921
##
## Initial states:
## l = 10.0301
##
## sigma: 0.018
##
## AIC AICc BIC
## 842.5236 842.5910 854.1819fit.aa## Series: train.ts
## ARIMA(0,1,1)(1,0,2)[12]
##
## Coefficients:
## ma1 sar1 sma1 sma2
## -0.1335 0.2058 -0.3368 -0.0952
## s.e. 0.0527 0.3982 0.3985 0.0844
##
## sigma^2 estimated as 0.02848: log likelihood=130.99
## AIC=-251.99 AICc=-251.82 BIC=-232.57f.nn<-forecast(fit.nn)
f.ets<-forecast(fit.ets)
f.aa<-forecast(fit.aa)
plot(f.nn)
plot(f.ets)
plot(f.aa)
acc.nn<-accuracy(f.nn, test.ts)
acc.ets<-accuracy(f.ets, test.ts)
acc.aa<-accuracy(f.aa, test.ts)
acc.nn## ME RMSE MAE MPE MAPE
## Training set 0.000406133 0.02753348 0.01817281 0.001532665 0.1988821
## Test set -1.117671454 1.24337777 1.11767145 -14.761759556 14.7617596
## MASE ACF1 Theil's U
## Training set 0.0441407 -0.007520579 NA
## Test set 2.7147596 0.306751206 2.172215acc.ets## ME RMSE MAE MPE MAPE MASE
## Training set -0.003950651 0.1703173 0.1249332 -0.06008919 1.32635 0.3034556
## Test set -0.893255366 1.0324101 0.8979587 -11.88304818 11.93647 2.1810900
## ACF1 Theil's U
## Training set 0.005904945 NA
## Test set 0.261105252 1.799568acc.aa## ME RMSE MAE MPE MAPE MASE
## Training set -0.005348857 0.1675941 0.1215799 -0.07790713 1.290701 0.2953106
## Test set -0.920190686 1.0598057 0.9267680 -12.23296324 12.307635 2.2510661
## ACF1 Theil's U
## Training set -0.002900959 NA
## Test set 0.244090380 1.844597train.ts<-window(mydata, end=c(2020,12))
test.ts<-window(mydata,start=c(2021,01))
fit.nn<-nnetar(train.ts)
fit.ets<-ets(train.ts)
fit.aa<-auto.arima(train.ts)
fit.nn## Series: train.ts
## Model: NNAR(13,1,7)[12]
## Call: nnetar(y = train.ts)
##
## Average of 20 networks, each of which is
## a 13-7-1 network with 106 weights
## options were - linear output units
##
## sigma^2 estimated as 0.01774fit.ets## ETS(A,N,N)
##
## Call:
## ets(y = train.ts)
##
## Smoothing parameters:
## alpha = 0.8101
##
## Initial states:
## l = 10.0401
##
## sigma: 0.217
##
## AIC AICc BIC
## 1069.068 1069.133 1080.825fit.aa## Series: train.ts
## ARIMA(0,1,1)(0,0,1)[12]
##
## Coefficients:
## ma1 sma1
## -0.2026 -0.1380
## s.e. 0.0553 0.0651
##
## sigma^2 estimated as 0.04661: log likelihood=43.16
## AIC=-80.33 AICc=-80.26 BIC=-68.58f.nn<-forecast(fit.nn)
f.ets<-forecast(fit.ets)
f.aa<-forecast(fit.aa)
plot(f.nn)
plot(f.ets)
plot(f.aa)
acc.nn<-accuracy(f.nn, test.ts)
acc.ets<-accuracy(f.ets, test.ts)
acc.aa<-accuracy(f.aa, test.ts)acc.nn## ME RMSE MAE MPE MAPE
## Training set 0.000265229 0.1331862 0.09076487 -0.03385538 0.9900594
## Test set -1.289512513 1.3513405 1.28951251 -16.32514288 16.3251429
## MASE ACF1 Theil's U
## Training set 0.2082923 -0.007618107 NA
## Test set 2.9592453 0.494653058 7.820522acc.ets## ME RMSE MAE MPE MAPE MASE
## Training set -0.007466718 0.2164075 0.1332672 -0.1255967 1.463752 0.3058290
## Test set 0.103714390 0.1996463 0.1475278 1.2680161 1.841490 0.3385551
## ACF1 Theil's U
## Training set 0.0128053 NA
## Test set 0.2125663 1.10871acc.aa## ME RMSE MAE MPE MAPE MASE
## Training set -0.008184355 0.2150265 0.1324155 -0.1347985 1.455732 0.3038744
## Test set -0.020051046 0.1801979 0.1534100 -0.2942470 1.932382 0.3520539
## ACF1 Theil's U
## Training set 0.01234188 NA
## Test set 0.13641492 0.9976622Using RMSE as my measure, since it, being square root of the variance of the residuals indicates thehow close the predicted value was to the actual value, will give me a good idea of which model is most accurate. The lowest value meaning is was closest to the actual data was the ARIMA mode. Given the volitality between that and the ETS model are similar I believe the ARIMA model best.