Calculate interval forecast width

Calculate the mean width of the prediction intervals on the validation set. If window is not NULL, a matrix of the rolling means of the 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".
...: Time-series matrices LOWER and UPPER if object is missing. They may also be lists keyed by confidence level.
level: Target confidence level for the prediction intervals. Only one level can be specified. Defaults to 95.
includemedian: If TRUE, the median interval width will also be returned. Defaults to FALSE.
window: If not NULL, the rolling mean (and the rolling median if applicable) matrix for the interval width will also be returned. Defaults to NULL.
na.rm: A logical indicating whether NA values should be stripped before the rolling mean and rolling median computation proceeds. Defaults to FALSE.

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 the 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 the interval width will be returned.

Examples

# Simulate time series from an AR(2) model
library(forecast)
set.seed(1)
series <- arima.sim(n = 200, list(ar = c(0.8, -0.5)), sd = sqrt(1))

# Cross-validation forecasting with a rolling window
far2 <- function(x, h, level) {
  Arima(x, order = c(2, 0, 0)) |>
    forecast(h = h, level)
}
fc <- cvforecast(series, forecastfun = far2, h = 3, level = 95, window = 50)

# Mean and rolling mean width for interval forecasts on validation set
wid_fc <- width(fc, level = 95, window = 50)
str(wid_fc)
#> List of 3
#>  $ width   : Time-Series [1:153, 1:3] from 51 to 203: 3.66 3.67 3.64 3.6 3.59 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "h=1" "h=2" "h=3"
#>  $ mean    : Named num [1:3] 3.72 4.69 4.76
#>   ..- attr(*, "names")= chr [1:3] "h=1" "h=2" "h=3"
#>  $ rollmean: Time-Series [1:104, 1:3] from 100 to 203: 3.65 3.65 3.63 3.63 3.62 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:3] "h=1" "h=2" "h=3"
#>  - attr(*, "class")= chr "width"

# Width calculated directly from interval components
width(LOWER = fc$LOWER, UPPER = fc$UPPER, level = 95)
#> Mean width:
#>      h=1      h=2      h=3 
#> 3.720038 4.692975 4.757742

Usage

Arguments

Value

See also

Examples