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

Slides for seminar

Download pdf

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 19 May.
  • GA4 is due on Monday 26 May.