Data

The package includes two data sets,auto and raf. Each data set is saved as a tsibble object, which is a tidy data structure for time series data. The identifiers of the time series are stored in the series_id column. Time indices are stored in the index column. The observed values are stored in the value column.

In this vignette, we use a subset sampling 200 time series from the auto data set, which contains 3000 time series of monthly sales of spare parts for cars. We use the filter() function to select the desired time series. Each time series is composed by 24 observations spanning from January 2010 to December 2011.

data(auto)
idx <- paste0("TS", sample(3000, 200))
data <- auto |>
  dplyr::filter(series_id %in% idx)

Example time series from the auto data set

Fitting and forecasting

The package provides several models from the literature, including:

• BETANBB()
• EMPDISTR()
• GAMPOISB()
• HSPES()
• MARWAL()
• NEGBINES()
• VZ()
• WSS()

Moreover, two novel methods are implemented:

• TWEES()
• STATICDISTR()

See the documentation for details on each function.

Before fitting the methods, we use the filter() function to drop the last 6 observation from each time series, which will be used for evaluating the forecasts. The methods are fitted using the model() function. In this vignette, we only use a pool of 4 models, two of which are the novel ones.

fit <- data |>
  dplyr::filter(index <= tsibble::yearmonth("2011 June")) |>
  fabletools::model(
    betanbb = BETANBB(value),
    staticdistr = STATICDISTR(value),
    twees = TWEES(value),
    wss = WSS(value)
  )

Forecasts are generated using the forecast() function, which produces a fable object containing the forecasts and their associated uncertainty. Other than the time series identifiers and the time indices, it contains a .model column that indicates the method used to generate the forecasts, a value column storing the predictive distributions (implemented as distributional objects), and a .mean column for the point forecast (the mean). We generate forecasts for the next 6 months.

fc <- fit |>
  fabletools::forecast(h = "6 months")

Evaluation

We evaluate the forecasts using the accuracy() function: among the different scoring rules, we use RMSSE for mean forecasts, and the pinball loss for quantile forecasts. To compare the performance of forecasting methods, we group the scores by model (via group_by()) and we aggregate them using the mean (via summarise()).

results <- fc |>
  fabletools::accuracy(data, measures = list(
    RMSSE = fabletools::RMSSE, 
    pinball_loss = fabletools::pinball_loss
    )) |>
  dplyr::group_by(.model) |>
  dplyr::summarise(
    RMSSE = mean(RMSSE), 
    pinball_loss  = mean(pinball_loss)
    )

Example forecast for one time series