Do the k largest weights sum up to less than p% of the total weights? — k_largest_weights_sum_to_less_than_p

Use this function to dynamically set observation_driven based on the fitted model's weights.

Usage

k_largest_weights_sum_to_less_than_p_percent(weights, k, p)

Arguments

weights: A vector of weights that sum to 1, as part of the model object returned by learn_weights()
k: The number of weights to consider, in decreasing order of their size
p: The threshold of cumulative probability under which the k weights might be

Value

A logical of length 1

Details

This is useful to judge whether a trained threedx model's prediction is the combination of at least a few historical observations. When using observation_driven during prediction, prediction intervals collapse to a single point when a single historical observation has (close to) 100% of the weights (which happens, for example, for the random walk or seasonal naive models). In those cases it can be better to switch to observation_driven = FALSE to get a non-collapsed prediction interval based on sampling residuals.

k_largest_weights_sum_to_less_than_p_percent() can be used to make this switch dynamically, based on the fitted weights. See also the examples below.

Examples

k_largest_weights_sum_to_less_than_p_percent(
  weights = c(0.02, 0.05, 0.05, 0.04, 0.8, 0.03, 0.01),
  k = 3,
  p = 0.9
)
#> [1] TRUE

k_largest_weights_sum_to_less_than_p_percent(
  weights = c(0.02, 0.05, 0.05, 0.04, 0.8, 0.03, 0.01),
  k = 4,
  p = 0.9
)
#> [1] FALSE

# Now apply it dynamically during prediction to set `observation_driven`

set.seed(9284)
y <- stats::rpois(n = 55, lambda = pmax(0.1, 1 + 10 * sinpi((5 + 1:55 )/ 6)))

model <- learn_weights(
  y = y,
  alphas_grid = list_sampled_alphas(
    n_target = 1000L,
    include_edge_cases = TRUE
  ),
  period_length = 12L,
  loss_function = loss_mae
)

forecast <- predict(
  object = model,
  horizon = 12L,
  n_samples = 2500L,
  innovation_function = draw_normal_with_zero_mean,
  observation_driven = k_largest_weights_sum_to_less_than_p_percent(
    weights = model$weights,
    k = 4,
    p = 0.95
  )
)

print(forecast$observation_driven)
#> [1] TRUE