Week 3: Time series decomposition

Tutorial exercises

• Complete Exercises 6, 7, 11 from Section 2.10 of the book.
• Tutorial learning objectives.
• Week 3 Tutorial Solution.html

What you will learn this week

• Transforming data to remove some sources of variation
• Decomposing a time series into trend-cycle, seasonal and remainder components
• Seasonal adjustment

Pre-seminar activities

Read Chapter 3 of the textbook and watch all embedded videos

Slides for seminar

Download pdf

Lectorial activities

1. Find an appropriate Box-Cox transformation in order to stabilise the variance for Gas production from aus_production.

2. Why is a Box-Cox transformation unhelpful for the canadian_gas data?

3. Produce the following decomposition for the number (in thousands) of of people employed in Retail Trade in the US

   us_retail_employment <- us_employment |>
     filter(year(Month) >= 1990, Title == "Retail Trade") |>
     select(-Series_ID)
   
   dcmp <- us_retail_employment |>
           model(stl = STL(Employed)) 

   1. Plot the decomposition.

   2. Fit the trend component over the data [Hint: you can use autolayer() to add trend to the plot above. trend is one of the variables returned by STL(). ]

   3. Fit the trend and the seasonally adjusted [Hint: seas_adjust is one of the variables returned by STL. ]

   4. How does the seasonal shape change over time? [Hint: Try plotting the seasonal component using gg_season().]

   5. What happens as you change the values of the two window arguments?

   6. Can you produce a plausible seasonally adjusted series?

4. Exam 2024

   • Section A: Q6 (just for information at the moment)
   • Section B: Q1, Q2

Seminar code

week3.R

Assignments

• GA1 is due on Monday 24 March.