4.1 Some simple statistics

Any numerical summary computed from a time series is a feature of that time series — the mean, minimum or maximum, for example. These can be computed using the features() function. For example, let’s compute the means of all the series in the Australian tourism data.

tourism |>
  features(Trips, list(mean = mean)) |>
  arrange(mean)
#> # A tibble: 304 × 4
#>    Region          State              Purpose   mean
#>    <chr>           <chr>              <chr>    <dbl>
#>  1 Kangaroo Island South Australia    Other    0.340
#>  2 MacDonnell      Northern Territory Other    0.449
#>  3 Wilderness West Tasmania           Other    0.478
#>  4 Barkly          Northern Territory Other    0.632
#>  5 Clare Valley    South Australia    Other    0.898
#>  6 Barossa         South Australia    Other    1.02 
#>  7 Kakadu Arnhem   Northern Territory Other    1.04 
#>  8 Lasseter        Northern Territory Other    1.14 
#>  9 Wimmera         Victoria           Other    1.15 
#> 10 MacDonnell      Northern Territory Visiting 1.18 
#> # … with 294 more rows

Here we see that the series with least average number of visits was “Other” visits to Kangaroo Island in South Australia.

Rather than compute one feature at a time, it is convenient to compute many features at once. A common short summary of a data set is to compute five summary statistics: the minimum, first quartile, median, third quartile and maximum. These divide the data into four equal-size sections, each containing 25% of the data. The quantile() function can be used to compute them.

tourism |> features(Trips, quantile)
#> # A tibble: 304 × 8
#>    Region         State           Purpose    `0%`  `25%`   `50%`  `75%` `100%`
#>    <chr>          <chr>           <chr>     <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#>  1 Adelaide       South Australia Busine…  68.7   134.   153.    177.   242.  
#>  2 Adelaide       South Australia Holiday 108.    135.   154.    172.   224.  
#>  3 Adelaide       South Australia Other    25.9    43.9   53.8    62.5  107.  
#>  4 Adelaide       South Australia Visiti… 137.    179.   206.    229.   270.  
#>  5 Adelaide Hills South Australia Busine…   0       0      1.26    3.92  28.6 
#>  6 Adelaide Hills South Australia Holiday   0       5.77   8.52   14.1   35.8 
#>  7 Adelaide Hills South Australia Other     0       0      0.908   2.09   8.95
#>  8 Adelaide Hills South Australia Visiti…   0.778   8.91  12.2    16.8   81.1 
#>  9 Alice Springs  Northern Terri… Busine…   1.01    9.13  13.3    18.5   34.1 
#> 10 Alice Springs  Northern Terri… Holiday   2.81   16.9   31.5    44.8   76.5 
#> # … with 294 more rows

Here the minimum is labelled 0% and the maximum is labelled 100%.