Hyndman Forecasting - Section 3.7 Exercises (1–4)
Sachi Kapoor
February 25, 2026
library(fpp3)1 Exercise 3.7.1
Prompt: Consider the GDP information in
global_economy. Plot the GDP per capita for each country
over time. Which country has the highest GDP per capita? How has this
changed over time?
# GDP per capita over time (all countries) — can be busy but should run
gdp_pc <- global_economy |>
filter(!is.na(GDP), !is.na(Population)) |>
mutate(GDP_per_capita = GDP / Population) |>
select(Country, Year, GDP_per_capita)
autoplot(gdp_pc, GDP_per_capita) +
labs(title = "GDP per capita by country over time", y = "GDP per capita", x = "Year")
# NOTE: gdp_pc is a tsibble (Country key, Year index). To group by Year, convert to a tibble first.
gdp_pc_tbl <- gdp_pc |> as_tibble()
# Country with the highest GDP per capita each year
top_by_year <- gdp_pc_tbl |>
group_by(Year) |>
slice_max(GDP_per_capita, n = 1, with_ties = FALSE) |>
ungroup()
head(top_by_year, 15)## # A tibble: 15 × 3
## Country Year GDP_per_capita
## <fct> <dbl> <dbl>
## 1 United States 1960 3007.
## 2 United States 1961 3067.
## 3 United States 1962 3244.
## 4 United States 1963 3375.
## 5 United States 1964 3574.
## 6 Kuwait 1965 4429.
## 7 Kuwait 1966 4556.
## 8 United States 1967 4336.
## 9 United States 1968 4696.
## 10 United States 1969 5032.
## 11 Monaco 1970 12480.
## 12 Monaco 1971 13813.
## 13 Monaco 1972 16734.
## 14 Monaco 1973 21423.
## 15 Monaco 1974 22707.# Overall highest GDP per capita observation in the dataset
overall_top <- gdp_pc_tbl |>
slice_max(GDP_per_capita, n = 1, with_ties = FALSE)
overall_top## # A tibble: 1 × 3
## Country Year GDP_per_capita
## <fct> <dbl> <dbl>
## 1 Monaco 2014 185153.Write-up - State which country appears most often as
the top GDP per capita (from top_by_year). - Mention
whether leadership changes over time (some years a different country
leads).
2 Exercise 3.7.2
Prompt: For each series below, make a graph of the
data. If transforming seems appropriate, do so and describe the effect.
- United States GDP from global_economy - Slaughter of
Victorian “Bulls, bullocks and steers” in aus_livestock -
Victorian Electricity Demand from vic_elec - Gas production
from aus_production
2.1 (a) United States GDP (and optional log transform)
us_gdp <- global_economy |>
filter(Country == "United States") |>
select(Year, GDP)
autoplot(us_gdp, GDP) +
labs(title = "United States GDP", x = "Year", y = "GDP")
# Optional transform: log(GDP) often makes growth more linear
autoplot(us_gdp |> mutate(log_GDP = log(GDP)), log_GDP) +
labs(title = "United States GDP (log scale)", x = "Year", y = "log(GDP)")
2.2 (b) Victoria livestock: Bulls, bullocks and steers (and optional Box-Cox)
vic_bulls <- aus_livestock |>
filter(State == "Victoria", Animal == "Bulls, bullocks and steers") |>
select(Month, Count)
autoplot(vic_bulls, Count) +
labs(title = "Victoria: Bulls, bullocks and steers slaughter", x = "Month", y = "Count")
# Optional transform: Box-Cox using Guerrero method (works if positive)
lambda_bulls <- vic_bulls |> features(Count, guerrero) |> pull(lambda_guerrero)
autoplot(vic_bulls |> mutate(BC = box_cox(Count, lambda_bulls)), BC) +
labs(title = paste0("Box-Cox transformed (lambda=", round(lambda_bulls, 2), ")"),
x = "Month", y = "Transformed Count")
2.3 (c) Victorian electricity demand (use a small window)
# Plot only ONE WEEK to keep it light
vic_week <- vic_elec |>
filter(Time >= ymd_hms("2014-01-01 00:00:00"),
Time < ymd_hms("2014-01-08 00:00:00")) |>
select(Time, Demand)
autoplot(vic_week, Demand) +
labs(title = "Victoria electricity demand (one week sample)", x = "Time", y = "Demand (MWh)")
# Optional transform: log demand (Demand must be positive)
autoplot(vic_week |> mutate(log_Demand = log(Demand)), log_Demand) +
labs(title = "Victoria electricity demand (log scale, same week)", x = "Time", y = "log(Demand)")
2.4 (d) Gas production (and optional Box-Cox)
gas <- aus_production |>
select(Quarter, Gas)
autoplot(gas, Gas) +
labs(title = "Australian gas production", x = "Quarter", y = "Gas")
lambda_gas <- gas |> features(Gas, guerrero) |> pull(lambda_guerrero)
autoplot(gas |> mutate(BC = box_cox(Gas, lambda_gas)), BC) +
labs(title = paste0("Gas production (Box-Cox, lambda=", round(lambda_gas, 2), ")"),
x = "Quarter", y = "Transformed Gas")
Write-up - For each series, note trend/seasonality/variance changes. - If the transform helped, say it stabilized variance or made growth more linear.
3 Exercise 3.7.3
Prompt: Why is a Box-Cox transformation unhelpful
for the canadian_gas data?
autoplot(canadian_gas, Volume) +
labs(title = "Canadian gas", x = "Month", y = "Volume")
Write-up A Box–Cox transformation is mainly useful
to stabilize changing variance (e.g., when seasonal amplitude grows with
the level). For canadian_gas, the issue is not primarily
variance changing with the level — the series has strong seasonal
patterns and structural changes, and a simple power transform does not
remove seasonality or fix those structural shifts. As a result, Box–Cox
does not substantially simplify the pattern.
4 Exercise 3.7.4
Prompt: What Box–Cox transformation would you select for your retail data (from Exercise 7 in Section 2.10)?
# Choose ONE retail series (keep memory low)
retail <- aus_retail |>
filter(State == "New South Wales", Industry == "Department stores") |>
select(Month, Turnover)
lambda_retail <- retail |> features(Turnover, guerrero) |> pull(lambda_guerrero)
lambda_retail## [1] 0.2193207Write-up - Report the selected lambda from Guerrero’s method. - Mention that lambda near 0 corresponds to a log transform. - Briefly explain why (variance/seasonality grows with the level → transform helps stabilize).
5 Session Info
sessionInfo()## R version 4.5.2 (2025-10-31)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.4 LTS
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## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
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## time zone: UTC
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## attached base packages:
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## [5] tsibbledata_0.4.1 tsibble_1.2.0 ggplot2_4.0.2 lubridate_1.9.5
## [9] tidyr_1.3.2 dplyr_1.2.0 tibble_3.3.1 fpp3_1.0.3
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## loaded via a namespace (and not attached):
## [1] gtable_0.3.6 jsonlite_2.0.0 crayon_1.5.3
## [4] compiler_4.5.2 tidyselect_1.2.1 Rcpp_1.1.1
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