Week 4 Discussion - ARIMA vs ETS

Demetri Chokshi-Fox

Data from St. Louis FRED not seasonally adjusted unemployment rate for US

library(forecast)

## Warning: package 'forecast' was built under R version 3.5.3

library(readr)

## Warning: package 'readr' was built under R version 3.5.3

library(data.table)

## Warning: package 'data.table' was built under R version 3.5.3

library(fpp2)

## Warning: package 'fpp2' was built under R version 3.5.3

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 3.5.3

## Loading required package: fma

## Warning: package 'fma' was built under R version 3.5.3

## Loading required package: expsmooth

## Warning: package 'expsmooth' was built under R version 3.5.3

UNRATENSA <- read.csv("C:/Users/Demetri/Google Drive/Grad School/Forecasting and Predictive Analytics/UNRATENSA.csv")

Import Data, then create test and training sets

unemp = ts(UNRATENSA[,2], start = c(2004, 6), end = c(2019, 6), frequency = 12)
train = window(unemp, end = c(2018, 12))
test = window(unemp, start = c(2019, 1))

Forecasts

arimafc <- train %>% auto.arima() %>% forecast(h=6)
etsfc <- train %>% ets() %>% forecast(h=6)

autoplot(arimafc)

autoplot(etsfc)

Validation Testing

arimamse = mean((test-arimafc$mean)^2)
etsmse = mean((test-etsfc$mean)^2)
c(arimamse, etsmse)

## [1] 0.01969911 0.04393041

summary(arimafc)

## 
## Forecast method: ARIMA(0,1,1)(0,1,1)[12]
## 
## Model Information:
## Series: . 
## ARIMA(0,1,1)(0,1,1)[12] 
## 
## Coefficients:
##          ma1     sma1
##       0.1463  -0.8377
## s.e.  0.0655   0.0951
## 
## sigma^2 estimated as 0.03576:  log likelihood=33.72
## AIC=-61.45   AICc=-61.29   BIC=-52.18
## 
## Error measures:
##                       ME      RMSE       MAE         MPE     MAPE
## Training set -0.00597964 0.1808117 0.1339804 -0.02638067 2.185413
##                   MASE       ACF1
## Training set 0.1528258 0.03713663
## 
## Forecasts:
##          Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## Jan 2019       4.377625 4.135032 4.620219 4.006611 4.748640
## Feb 2019       4.241740 3.872719 4.610761 3.677371 4.806109
## Mar 2019       3.994060 3.531998 4.456123 3.287397 4.700724
## Apr 2019       3.491407 2.952123 4.030691 2.666644 4.316170
## May 2019       3.536321 2.929565 4.143076 2.608369 4.464273
## Jun 2019       3.983130 3.315690 4.650570 2.962368 5.003891

summary(etsfc)

## 
## Forecast method: ETS(M,Ad,A)
## 
## Model Information:
## ETS(M,Ad,A) 
## 
## Call:
##  ets(y = .) 
## 
##   Smoothing parameters:
##     alpha = 0.6538 
##     beta  = 0.1762 
##     gamma = 1e-04 
##     phi   = 0.9297 
## 
##   Initial states:
##     l = 5.425 
##     b = 0.0309 
##     s = -0.2411 -0.3052 0.1278 0.3642 0.4513 -0.2043
##            -0.2662 -0.3131 -0.1874 0.0712 0.2928 0.2101
## 
##   sigma:  0.027
## 
##      AIC     AICc      BIC 
## 282.7158 287.1004 339.6819 
## 
## Error measures:
##                        ME      RMSE       MAE         MPE     MAPE
## Training set -0.003573483 0.1631107 0.1262342 -0.03407441 2.048141
##                   MASE      ACF1
## Training set 0.1439901 0.1999058
## 
## Forecasts:
##          Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## Jan 2019       4.311199 4.162051 4.460347 4.083096 4.539301
## Feb 2019       4.231540 4.040980 4.422100 3.940104 4.522976
## Mar 2019       4.002166 3.768803 4.235529 3.645269 4.359063
## Apr 2019       3.575557 3.300177 3.850938 3.154399 3.996715
## May 2019       3.645786 3.321498 3.970074 3.149831 4.141742
## Jun 2019       4.102677 3.723614 4.481740 3.522950 4.682404

ARIMA Forecast has better MSE on test data, but ETS has a better RMSE when looking at information criterion.

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