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 x 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 x 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 Hil… South Australia  Busine…   0       0      1.26    3.92  28.6 
#>  6 Adelaide Hil… South Australia  Holiday   0       5.77   8.52   14.1   35.8 
#>  7 Adelaide Hil… South Australia  Other     0       0      0.908   2.09   8.95
#>  8 Adelaide Hil… South Australia  Visiti…   0.778   8.91  12.2    16.8   81.1 
#>  9 Alice Springs Northern Territ… Busine…   1.01    9.13  13.3    18.5   34.1 
#> 10 Alice Springs Northern Territ… 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%.