Calculate interval forecast width — width • conformalForecast

Calculate the mean width of prediction intervals on the validation set. If window is not NULL, a matrix of the rolling means of interval width is also returned. If includemedian is TRUE, the information of the median interval width will be returned.

Usage

width(
  object,
  ...,
  level = 95,
  includemedian = FALSE,
  window = NULL,
  na.rm = FALSE
)

Arguments

object: An object of class "cvforecast" or "cpforecast".
...: Additional inputs if object is missing.
level: Target confidence level for prediction intervals.
includemedian: If TRUE, the median interval width will also be returned.
window: If not NULL, the rolling mean (and rolling median if applicable) matrix for interval width will also be returned.
na.rm: A logical indicating whether NA values should be stripped before the rolling mean and rolling median computation proceeds.

Value

A list of class "width" with the following components:

width: Forecast interval width as a multivariate time series, where the \(h\)th column holds the interval width for the forecast horizon \(h\). The time index corresponds to the period for which the forecast is produced.
mean: Mean interval width across the validation set.
rollmean: If window is not NULL, a matrix of the rolling means of interval width will be returned.
median: Median interval width across the validation set.
rollmedian: If window is not NULL, a matrix of the rolling medians of interval width will be returned.

Examples

# Simulate time series from an AR(2) model
library(forecast)
series <- arima.sim(n = 1000, list(ar = c(0.8, -0.5)), sd = sqrt(1))

# Cross-validation forecasting with a rolling window of length 100
far2 <- function(x, h, level) {
  Arima(x, order = c(2, 0, 0)) |>
    forecast(h = h, level)
}
fc <- cvforecast(series, forecastfun = far2, h = 3, level = c(80, 95),
                 forward = TRUE, initial = 1, window = 100)

# Mean and rolling mean width for interval forecasts on validation set
wid_fc <- width(fc, level = 95, window = 100)
str(wid_fc)
#> List of 3
#>  $ width   : Time-Series [1:903, 1:3] from 101 to 1003: 4.01 4 4.01 4.02 4.02 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "h=1" "h=2" "h=3"
#>  $ mean    : Named num [1:3] 3.94 5.03 5.08
#>   ..- attr(*, "names")= chr [1:3] "h=1" "h=2" "h=3"
#>  $ rollmean: Time-Series [1:804, 1:3] from 200 to 1003: 3.93 3.93 3.93 3.93 3.93 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "h=1" "h=2" "h=3"
#>  - attr(*, "class")= chr "width"