ETS model

Introduction

This is a dataset I have been using, which is Egg Laying Hens in the U.S. published by the USDA at the beginning of each month. I test ETS modeling and data manipulation using different techniques.

Quick Data Exploration

#convert to tsibble and plot

egg_layers <- egg_layers %>%
  mutate(Date = yearmonth(Date)) %>%
  as_tsibble(index = Date)

egg_layers %>%
  autoplot(layers) +
  labs(x = "Month",
       y = "Egg Laying Hens",
       title = "Table Egg Laying Hens in the U.S.",
       subtitle = "On-hand first of the month"
       )

#Split the data

train_end_date <- round(length(rownames(egg_layers))*0.8,0)
test_start_date <- train_end_date+1

egg_layers_train <-egg_layers[1:train_end_date,]
egg_layers_test <-egg_layers[test_start_date:length(rownames(egg_layers)),]

ETS Model 1.0

This is a ts appraoch as opposed to a tsibble.

m.stats <- function(m.n, m.s){ # model.type, model.stats
  aic <- round(m.s$aic, 2)
  aicc <- round(m.s$aicc, 2)
  bic <- round(m.s$bic, 2)
  
  return(c(m.n, aic,aicc,bic))
}


myts.3 <-ts(egg_layers$layers, frequency = 12)
tsdisplay(myts.3)

# ANN
ANN <-ets(myts.3, model="ANN")
autoplot(ANN)

#ANA
ANA <-ets(myts.3, model="ANA")
autoplot(ANA)

#AAN
AAN <-ets(myts.3, model = "AAN")
autoplot(AAN)

#AAA
AAA <-ets(myts.3, model = "AAA")
autoplot(AAA)

#MAM
MAM <-ets(myts.3, model = "MAM")

autoplot(MAM)

Test ETS Models 1.0, and forecasts

#Test the models
m.e <- data.frame(matrix(ncol=4)) # model.evaluation
names(m.e)[1:4] <- c("Model", "aic", "aicc", "bic")

m.e[1,] <- m.stats("ANN", ANN)
m.e[2,] <- m.stats("ANA", ANA)
m.e[3,] <- m.stats("AAN", AAN)
m.e[4,] <- m.stats("AAA", AAA)
m.e[5,] <- m.stats("MAM", MAM)

m.e %>%
  kbl()%>%
  kable_material(c("striped","hover", full_width = T))

Model	aic	aicc	bic
ANN	714.32	714.58	722.05
ANA	706.19	712.12	744.81
AAN	713	713.94	728.45
AAA	712.36	720.1	756.13
MAM	724.26	733.03	770.6

autoplot(ANA)

myts.3 <- ts(egg_layers, frequency = 13)
test <- forecast(ANA)

autoplot(test) + 
  labs(y="Million Egg Laying Hens"
       , x = "Date") +
  theme_ipsum_es()

### Unable to make dates appear on the chart

ETS Model 2.0

A tsibble approach.

egg_lay_ETS <-
  egg_layers_train %>% 
  model(ETS_AAM = ETS(layers ~ error("A") + trend("A") + season("M")),
        ETS_AAA = ETS(layers ~ error("A") + trend("A") + season("A")),
        ETS_MNA = ETS(layers ~ error("M") + trend("N") + season("M")),
        ETS_ANA = ETS(layers ~ error("A") + trend("N") + season("A")))

#Metrics
metrics<-glance(egg_lay_ETS)

metrics%>%
  kbl()%>%
  kable_material(c("striped","hover", full_width = T))

.model	sigma2	log_lik	AIC	AICc	BIC	MSE	AMSE	MAE
ETS_AAM	26.3234305	-288.5062	611.0123	621.2123	651.0764	20.92375	43.91165	3.2226647
ETS_AAA	17.0683374	-271.6100	577.2200	587.4200	617.2841	13.56714	32.35771	2.3346500
ETS_MNA	0.0001644	-271.0800	572.1600	579.9020	607.5107	12.50975	32.08485	0.0072078
ETS_ANA	14.7381198	-267.1235	564.2470	571.9889	599.5976	12.09282	30.74961	2.2039305

#knitr::kable(glance(egg_lay_ETS), "html")

ETS model 2.0 test, and forecast.

#Plot forecast using ANA from Above

egg_lay_fcst <-
  egg_lay_ETS %>%
  forecast(h = length(rownames(egg_layers_test)))

egg_lay_fcst %>%
  filter(.model == "ETS_ANA") %>%
  autoplot(egg_layers_test) +
  labs(x = "Month",
       y = "Egg Laying Hens",
       title = "Egg Laying Hens",
       subtitle = "ETS using ANA"
       , legend = TRUE) +
  theme_ipsum_es()

Conclusion

The model that had the best performance was ETS ANA.Although there appears to be a trend, we can see that the mean appears constant according to the test–although not conclusive. I will try an ARIMA model instead in another post.