Week 11: Dynamic regression

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 activities

Read Chapter 10 of the textbook and watch all embedded videos

Exercises (on your own or in tutorial)

Complete Exercises 1-7 from Section 7.10 of the book.

Slides for seminar

Download pdf

Seminar activities

Repeat the daily electricity example, but instead of using a quadratic function of temperature, use a piecewise linear function with the “knot” around 20 degrees Celsius (use predictors Temperature & Temp2). How can you optimize the choice of knot?

The data can be created as follows.

vic_elec_daily <- vic_elec |>
  filter(year(Time) == 2014) |>
  index_by(Date = date(Time)) |>
    Demand = sum(Demand)/1e3,
    Temperature = max(Temperature),
    Holiday = any(Holiday)
  ) |>
    Temp2 = I(pmax(Temperature-20,0)),
    Day_Type = case_when(
      Holiday ~ "Holiday",
      wday(Date) %in% 2:6 ~ "Weekday",
      TRUE ~ "Weekend"

Repeat but using all available data, and handling the annual seasonality using Fourier terms.