Exponential smoothing

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Four series, each from a different part of the Norwegian economy: how many people live here, what a US dollar costs in kroner, what it costs a bank to borrow overnight from Norges Bank, and how many nights people spent in Norwegian hotels. For each one, split into training and test data, fit a few candidate ETS() specifications, forecast, and check against the test set what actually helped.

The data

install.packages("remotes")
remotes::install_github("holleland/ban430data")
library(fpp3)
library(ban430data)
data(decomposition)
data(ets_lab)
Object Series Contents
population_no 1 Norway’s national population at the start of each quarter, 1997 Q4 → today
exchange_usdnok 2 average monthly USD/NOK spot exchange rate, 2010 → today
policy_rate_no 3 Norges Bank’s key policy rate, monthly, 2010 → today
hotel_guestnights 4 monthly guest nights at hotels and similar accommodation, all of Norway, 1986 → today

Cheat sheet: ETS() syntax

Term Syntax
Simple exponential smoothing ETS(y ~ error("A") + trend("N") + season("N"))
Holt’s linear trend ETS(y ~ error("A") + trend("A") + season("N"))
Damped trend ETS(y ~ error("A") + trend("Ad") + season("N"))
Holt-Winters, additive season ETS(y ~ error("A") + trend("A") + season("A"))
Holt-Winters, multiplicative season ETS(y ~ error("M") + trend("A") + season("M"))
Let ETS() choose everything ETS(y)
Fit model(name = ETS(...))
Inspect a fitted model report(fit) or fit %>% select(name) %>% report()
Forecast a known window forecast(fit, new_data = test)
Accuracy vs. the actuals accuracy(fc, full_data)

Series 1: Norwegian population

Quarterly, 1997 Q4 → today.

train_pop <- population_no %>% filter(quarter < yearquarter("2023 Q3"))
test_pop  <- population_no %>% filter(quarter >= yearquarter("2023 Q3"))

Fit a few candidate ETS() specifications on train_pop, forecast test_pop, and compare their accuracy.

💡 Code hint 
fit_pop <- train_pop %>%
  model(
    SES    = ETS(population ~ error("A") + trend("N")  + season("N")),
    Holt   = ETS(population ~ error("A") + trend("A")  + season("N")),
    Damped = ETS(population ~ error("A") + trend("Ad") + season("N")),
    Auto   = ETS(population)
  )
fit_pop %>% forecast(new_data = test_pop) %>% accuracy(population_no) %>%
  select(.model, RMSE, MASE) %>% arrange(RMSE)

Print report() for the automatically selected model (fit_pop %>% select(Auto) %>% report()) and read off which components it actually contains.

Q: Which components — trend, damping, season — actually earned their place on the test set, and which just added complexity without improving the forecast?

Series 2: the USD/NOK exchange rate

Monthly, 2010 → today.

train_fx <- exchange_usdnok %>% filter(month < yearmonth("2025-09"))
test_fx  <- exchange_usdnok %>% filter(month >= yearmonth("2025-09"))

Fit a few candidate ETS() specifications on train_fx, forecast test_fx, and compare their accuracy.

💡 Code hint 
fit_fx <- train_fx %>%
  model(
    SES    = ETS(rate ~ error("A") + trend("N")  + season("N")),
    Holt   = ETS(rate ~ error("A") + trend("A")  + season("N")),
    Auto   = ETS(rate),
    Naive  = NAIVE(rate)
  )
fit_fx %>% forecast(new_data = test_fx) %>% accuracy(exchange_usdnok) %>%
  select(.model, RMSE, MASE) %>% arrange(RMSE)

Print report() for the automatically selected model and for Naive’s closest competitor — what do their fitted parameters have in common?

Q: Did adding a trend component help here, hurt, or make no real difference? What does that tell you about which component actually matters for this series?

Series 3: Norges Bank’s key policy rate

Monthly. Train on data only through the end of 2023, and forecast the two years after.

train_rate <- policy_rate_no %>% filter(month < yearmonth("2024-01"))
test_rate  <- policy_rate_no %>% filter(month >= yearmonth("2024-01"), month < yearmonth("2026-01"))

Fit a couple of candidate ETS() specifications on train_rate and forecast test_rate.

💡 Code hint 
fit_rate <- train_rate %>%
  model(
    Holt   = ETS(rate ~ error("A") + trend("A")  + season("N")),
    Damped = ETS(rate ~ error("A") + trend("Ad") + season("N"))
  )
fc_rate <- fit_rate %>% forecast(new_data = test_rate)
fc_rate %>% accuracy(policy_rate_no) %>% select(.model, RMSE, MASE)

Print report() for both models, then plot both forecasts against what actually happened:

fc_rate %>% autoplot(policy_rate_no %>% filter(month >= yearmonth("2022-01")), level = NULL)

Q: By how many percentage points do the two forecasts disagree two years out? What did the rate actually do? Which single component — trend or damping — is responsible for almost all of that gap?

Series 4: hotel guest nights

Monthly, 1986 → today. This is the one from the decomposition lecture.

hotel <- hotel_guestnights %>% rename(guests = `Guest nights`)

train_hotel <- hotel %>% filter(yearmonth < yearmonth("2024-07"))
test_hotel  <- hotel %>% filter(yearmonth >= yearmonth("2024-07"))

Fit a few candidate ETS() specifications on train_hotel, forecast test_hotel, and compare their accuracy.

💡 Code hint 
fit_hotel <- train_hotel %>%
  model(
    SES     = ETS(guests ~ error("A") + trend("N")  + season("N")),
    HW_add  = ETS(guests ~ error("A") + trend("A")  + season("A")),
    HW_mult = ETS(guests ~ error("M") + trend("A")  + season("M")),
    Auto    = ETS(guests)
  )
fit_hotel %>% forecast(new_data = test_hotel) %>% accuracy(hotel) %>%
  select(.model, RMSE, MASE) %>% arrange(RMSE)

Print report() for the automatically selected model.

Q: Adding a season component clearly matters here — but does it matter how you add it? Look back at the full series plot: is there anything around early 2020 that might explain why an additive vs. multiplicative season makes such a difference?

Wrap-up discussion

  • For each of the four series: which ETS components (trend, damping, season, and the choice between additive/multiplicative) actually mattered, and which ones didn’t move the needle? Is there a series where none of the extra components beat simple exponential smoothing?
  • In how many of your four series did ETS()’s own automatic pick actually win on the test set? Would you trust automatic selection for a model you had to actually deploy — or would you always want to check it against a held-out test set, and read its report(), first?
  • The policy-rate series trains right up to the peak of a rapid change. Real deployed forecasting systems don’t get to choose such a convenient cutoff — how would you know, in practice, that you were sitting at a turning point where an undamped trend was about to go badly wrong?
  • Which of today’s four series would you be comfortable handing a fully automatic ETS() pipeline for, with no human checking the forecast before it’s used? Which would you not — and what would you want a human to check first?