Workshop Activities: Week 3

Week 3 Mini-Studio

Note

Back to Week 3 overview

This page follows the same sequence as week3-code.R. It is designed as a stable seminar companion: read the code, run the matching block in R or RStudio, then answer the short prompts here in words. That keeps the focus on the class code, which is the style you are most likely to meet in the exam.

TipHow to use this page
  1. Open week3-code.R beside this page.
  2. Work through the sections in order.
  3. Run the matching block in RStudio.
  4. Use the prompts here to practise explanation and model choice, not just syntax.

A. Generate white noise

This section simulates white noise.

set.seed(100)
T=1000
my_data <- tsibble(t = seq(T), y = rnorm(T), index = t)
my_data |> autoplot(y)
my_data |> gg_tsdisplay(y, plot_type = "histogram")
NoteWhat this code is doing
  • Sets a random seed for reproducibility.
  • Generates 1000 random normal values as white noise.
  • Plots the time series and displays ACF/PACF with histogram.
NoteWhat to notice
  • The ACF should show no significant spikes (within blue lines).
  • Histogram should be approximately normal.

B. Generate random walk

Simulate a random walk.

set.seed(100)
T=1000
tsibble(t = seq(T), y = cumsum(rnorm(T)), index = t) |>
  gg_tsdisplay(y, plot_type = "histogram")
NoteWhat this code is doing
  • Generates a random walk by cumulative sum of random normals.
  • Displays the time series, ACF/PACF, and histogram.
NoteWhat to notice
  • The series wanders without returning to mean.
  • ACF decays slowly, indicating non-stationarity.

C. Plot US GDP

Plot raw GDP.

us_economy <- global_economy |>
  filter(Country == "United States")

us_economy |>
  autoplot(GDP)
NoteWhat this code is doing
  • Filters global_economy for US.
  • Plots GDP over time.
NoteWhat to notice
  • Look for increasing variance over time.

D. Plot log GDP

Apply log transformation.

us_economy |>
  autoplot(log(GDP))
NoteWhat this code is doing
  • Plots the natural log of GDP.
NoteWhat to notice
  • Variance may be more stable, but check if it’s appropriate.

E. Box-Cox transformations

Try Box-Cox with lambda 0 (log) and 0.3.

us_economy |> 
  autoplot(box_cox(GDP, 0))

us_economy |>
  autoplot(box_cox(GDP, 0.3))
NoteWhat this code is doing
  • Applies Box-Cox transformation with different lambdas.
  • Plots the transformed series.
NoteWhat to notice
  • Lambda 0.3 may stabilize variance better than log.

F. Guerrero method

Use Guerrero to find optimal lambda.

us_economy |> 
  features(GDP, guerrero) |> 
  pull(lambda_guerrero)
NoteWhat this code is doing
  • Computes the Guerrero lambda for Box-Cox.
NoteWhat to notice
  • This gives the recommended lambda value.

G. STL decomposition for US retail employment

Perform STL decomposition.

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

dcmp <- us_retail_employment |>
  model(stl = STL(Employed))
NoteWhat this code is doing
  • Filters US employment data for retail trade from 1990.
  • Fits STL decomposition.
NoteWhat to notice
  • STL decomposes into trend, seasonal, remainder.

H. Plot the decomposition

Visualize the components.

dcmp |> components() |> autoplot()
NoteWhat this code is doing
  • Plots the trend, seasonal, and remainder components.
NoteWhat to notice
  • Examine each component’s behavior.

I. Fit trend over data

Overlay trend on original data.

us_retail_employment |> 
  autoplot(Employed) +
  autolayer(dcmp |> components(), trend)
NoteWhat this code is doing
  • Plots original data with trend component overlaid.
NoteWhat to notice
  • How well the trend captures the overall movement.

J. Fit trend and seasonally adjusted

Plot trend and seasonally adjusted series.

us_retail_employment |> 
  autoplot(Employed) +
  autolayer(dcmp |> components(), trend) +
  autolayer(dcmp |> components(), season_adjust)
NoteWhat this code is doing
  • Adds the seasonally adjusted series to the plot.
NoteWhat to notice
  • Seasonally adjusted removes seasonal variation.

K. Seasonal shape over time

Plot seasonal component with gg_season.

dcmp |> components() |> gg_season(seasonal)
NoteWhat this code is doing
  • Plots the seasonal component by season.
NoteWhat to notice
  • How the seasonal pattern changes over years.

L. Experiment with window arguments

Change window values in STL.

# Example: change trend window
dcmp_alt <- us_retail_employment |>
  model(stl = STL(Employed ~ trend(window = 13) + season(window = 7)))
dcmp_alt |> components() |> autoplot()
NoteWhat this code is doing
  • Fits STL with different window sizes.
NoteWhat to notice
  • How window changes affect smoothness of components.

M. Plausible seasonally adjusted series

Assess the seasonally adjusted series.

NoteExam-style prompt

Evaluate if the seasonally adjusted series is plausible. Consider the trend and any remaining patterns.