Activities: Week 8

AUD exchange rates

The data set contains Australian dollar exchange rates from the start of 2023 to 22 April 2025.

library(fpp3)
aud_xr <- readRDS(url("https://bit.ly/aud_xr"))

1. How has the tsibble been indexed? Why wouldn’t Date be used for the index?

2. See what currencies are included:

   aud_xr |>
     distinct(Currency, Description)

3. Choose a currency and plot its exchange rate using gg_tsdisplay like this. Does it look stationary?

   aud_xr |>
     filter(Currency == ???) |>
     autoplot(Rate)

4. Now plot the first difference of the exchange rate. Does it look stationary?

   aud_xr |>
     filter(Currency == ???) |>
     autoplot(difference(Rate))

5. Repeat for another couple of exchange rates. Does differencing always result in a stationary series? Why?

6. If we used the unitroot_ndiffs() function, would it give the same answer?

   aud_xr |>
     features(Rate, unitroot_ndiffs)

Tasmanian accommodation takings

Let’s extract the Tasmanian data from aus_accommodation. Check the help to see what this data set contains.

tas_takings <- aus_accommodation |>
  filter(State == "Tasmania") |>
  select(Takings)

We will try to find transformations that make this series stationary.

1. First, try to stabilise the variance using a Box-Cox transformation.

   tas_takings |>
     autoplot(
       box_cox(Takings, lambda = ???)
     )

2. Then, try to stabilise the mean using seasonal differencing.

   tas_takings |>
     autoplot(
       box_cox(Takings, lambda = ???) |>
       difference(lag = ???)
     )

3. If that doesn’t work, try a first difference as well.

   tas_takings |>
     autoplot(
       box_cox(Takings, lambda = ???) |>
       difference(lag = ???) |>
       difference(lag = ???)
     )

   The final transformed series should appear stationary.

4. Check its ACF.

   tas_takings |>
     ACF(
       box_cox(Takings, lambda = ???) |>
       difference(lag = ???) |>
       difference(lag = ???)
     ) |>
     autoplot()

   What do you conclude?

5. Now use the unitroot_ndiffs and unitroot_nsdiffs functions to check what differences they would suggest:

   tas_takings |>
     features(
       box_cox(Takings, lambda = ???),
       unitroot_nsdiffs
     )

   tas_takings |>
     features(
       box_cox(Takings, lambda = ???) |> difference(lag = ???),
       unitroot_nsdiffs
     )

   Does it suggest the same number of differencing as you did? Why/why not?