Week 11: Dynamic regression

Tutorial exercises

What you will learn this week

  • How to combine regression models with ARIMA models to form dynamic regression models
  • Dynamic harmonic regression to handle complex seasonality
  • Lagged predictors

Pre-class seminar

Read Chapter 10 of the textbook and watch all embedded videos

Seminar activities

  1. Review the model for US gasoline data from last week to now be a dynamic harmonic regression model.

  2. Turn the half hourly electricity data into daily data using the following code. Try and understand what each line does.

    vic_elec_daily <- vic_elec |>
  index_by(Date = date(Time)) |>    # index by date to turn into daily
  summarise(                        # summarise() below
    Demand = sum(Demand)/1e3,       # Total daily and scaling Mega to Gigawatts
    Temperature = max(Temperature), # take highest temperature for the day
    Holiday = any(Holiday)          # Hol for any half hour is Hol for day
  ) |> # create new variable Day_Type
mutate(Day_Type = case_when(       # Separate weekdays, weekends and holidays
  Holiday ~ "Holiday",             # If Holiday=TRUE call it a Holiday
  wday(Date) %in% 2:6 ~ "Weekday", # wday() returns 1:7 starting from a Sunday
  TRUE ~ "Weekend"                 # Call everything else a weekend
  ))

    Explore the seasonal patterns.

    1. Fit an ETS, ARIMA and a dynamic harmonic regression model using the following code:
    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))
  )

    Explore the model fits and residuals.

    1. Generate forecast for 14-days-ahead using the following code.
    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"
    )
  )

  3. Exam 2024

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

  4. Exam 2023

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

Seminar code

week11.R

Assignments

  • IA4 is due on Monday 18 May.
  • GA4 is due on Monday 25 May.

Weekly quiz