Workshop Activities: Week 11

Week 11 Mini-Studio

Note

Back to Week 11 overview

This page follows week11.R. Focus on dynamic harmonic regression and forecast scenarios with external regressors.

A. Extend gasoline model to dynamic harmonic regression

Revisit the weekly gasoline setup from week 10 and add ARIMA error structure as shown in week11.R.

What to notice

Why does adding ARIMA errors improve over pure harmonic regression?
Which residual patterns remain after adding dynamics?

B. Convert half-hourly electricity to daily series

vic_elec_daily <- vic_elec |>
  index_by(Date = date(Time)) |>
  summarise(
    Demand = sum(Demand) / 1e3,
    Temperature = max(Temperature),
    Holiday = any(Holiday)
  ) |>
  mutate(
    Day_Type = case_when(
      Holiday ~ "Holiday",
      wday(Date) %in% 2:6 ~ "Weekday",
      TRUE ~ "Weekend"
    )
  )

What to notice

Understand each transformation and why daily aggregation is useful.
Compare weekly and yearly seasonal patterns after aggregation.

C. Compare ETS, ARIMA, and DHR for electricity demand

elec_fit <- vic_elec_daily |>
  model(
    ets = ETS(Demand),
    arima = ARIMA(log(Demand)),
    dhr = ARIMA(log(Demand) ~ Temperature + I(Temperature^2) +
      (Day_Type == "Weekday") +
      fourier(period = "year", K = 4))
  )

accuracy(elec_fit)

What to notice

Which model best captures temperature effects and calendar structure?
Evaluate fit and residual diagnostics, not only training accuracy.

D. Build and forecast a 14-day scenario

vic_elec_future <- new_data(vic_elec_daily, 14) |>
  mutate(
    Temperature = c(rep(32, 7), rep(25, 7)),
    Holiday = c(TRUE, rep(FALSE, 13)),
    Day_Type = case_when(
      Holiday ~ "Holiday",
      wday(Date) %in% 2:6 ~ "Weekday",
      TRUE ~ "Weekend"
    )
  )

Then run the forecast blocks in week11.R.

Exam Practice

2024: - Section A: Q4 - Section B: Q3 (i-j) - Section E: all questions

2023: - Section A: Q6 - Section B: Q3 (i-j) - Section D: all questions - Section E: all questions