Discussion 2

Author

Sam Kuhn

Pick a time series dataset of interest to you. Using this data (be sure to sort in ascending order), build two or three ETS models. Which performs better? What explanation might explain that?

Collect data from FRED

Seasonally un-adjusted quarterly PCE

library(tidyverse)
library(fpp3)
library(fredr)
library(ggthemes)
pce <- fredr(
  series_id = "NA000349Q",
  observation_start = as.Date("1950-01-01"),
  observation_end = as.Date("2023-10-01"),
  frequency = "q", # quarterly
  units = "lin"
) |> 
  select(date, value) |> 
  mutate(date = tsibble::yearquarter(date)) |> 
  as_tsibble()

Plot

Change points -

Decline during GFC
Increase post-COVID pandemic recession

pce |> 
  ggplot(aes(date, value)) +
  geom_line(linewidth = 1.25) +
  scale_x_yearquarter(
    breaks = scales::breaks_width("10 years")
  ) +
  scale_y_continuous(
    breaks = scales::breaks_width(750000),
    labels = scales::label_dollar()
  ) +
  labs(
    title = "Personal consumption expenditures",
    subtitle = "Not seasonally adjusted, in billions of dollars"
  ) +
  ggthemes::theme_economist()

STL decomposition

decomp <- pce |> 
  model(stl = STL(value))
decomp |> 
  components() |> 
  autoplot()

pce |> 
  autoplot(value) +
  autolayer(components(decomp), season_adjust, color = "darkred") +
  scale_y_continuous(
    breaks = scales::breaks_width(500000),
    labels = scales::label_dollar()
  ) +
  ggthemes::theme_economist()

Train/test splits

train <- pce |> 
  filter_index("1950 Q1" ~ "2000 Q1")

fit <- train |> 
  model(
    additive = ETS(value ~ error("A") + trend("A") + season("A")),
    multiplicative = ETS(value ~ error("M") + trend("M") + season("M")),
    additive_errors = ETS(value ~ error("A") + trend("N") + season("N")),
    mult_errors = ETS(value ~ error("M") + trend("N") + season("N"))
  )

Forecast

ets_fc <- fit |> 
  forecast(h = 92)

ets_fc |> 
  autoplot(
    pce,
    level = NULL
  ) +
  ggthemes::theme_economist()

Model performance

fit |> report()

# A tibble: 4 × 9
  .model           sigma2 log_lik   AIC  AICc   BIC        MSE      AMSE     MAE
  <chr>             <dbl>   <dbl> <dbl> <dbl> <dbl>      <dbl>     <dbl>   <dbl>
1 additive        3.32e+7  -2270. 4557. 4558. 4587.  31924094.    4.97e7 3.64e+3
2 multiplicative  1.80e-4  -2173. 4365. 4366. 4394.  25961771.    4.27e7 9.13e-3
3 additive_errors 7.42e+8  -2585. 5175. 5176. 5185. 734928640.    1.14e9 1.91e+4
4 mult_errors     2.98e-3  -2453. 4913. 4913. 4923. 737952658.    1.16e9 4.73e-2

Forecast on full data set with additive model

additive_model <- pce |> 
  model(additive = ETS(value ~ error("A") + trend("A") + season("A")))

additive_model |> 
  forecast(h = 24) |> 
  autoplot(
    linewidth = 1.25
  ) +
  autolayer(
    pce,
    level = NULL,
    linewidth = 1.25,
    show_gap = FALSE
  ) +
  labs(
    title = "Forecasted PCE 24 months ahead using additive ETS"
  ) +
  ggthemes::theme_economist()