Accuracy measures for a cross-validation model and a conformal prediction model

Return a range of summary measures of the out-of-sample forecast accuracy. If x is given, the function also measures the test set forecast accuracy. If x is not given, the function only produces accuracy measures on the validation set.

Usage

# S3 method for class 'cvforecast'
accuracy(
  object,
  x,
  CV = TRUE,
  period = NULL,
  measures = interval_measures,
  byhorizon = FALSE,
  ...
)

# S3 method for class 'cpforecast'
accuracy(object, ...)

Arguments

object: An object of class "cvforecast" or "cpforecast".
x: An optional numerical vector containing the actual values of the same length as mean in object.
CV: If TRUE, the cross-validation forecast accuracy will be returned. Defaults to TRUE.
period: The seasonal period of the data. Defaults to NULL, in which case it is taken from the frequency of the series.
measures: A list of accuracy measure functions to compute (such as point_measures or interval_measures). Defaults to interval_measures.
byhorizon: If TRUE, accuracy measures will be calculated for each individual forecast horizon h separately. Defaults to FALSE.
...: Additional arguments depending on the specific measure.

Value

A matrix giving mean out-of-sample forecast accuracy measures.

Details

The measures calculated are:

ME: Mean Error
MAE: Mean Absolute Error
MSE: Mean Squared Error
RMSE: Root Mean Squared Error
MPE: Mean Percentage Error
MAPE: Mean Absolute Percentage Error
MASE: Mean Absolute Scaled Error
RMSSE: Root Mean Squared Scaled Error
Winkler: Winkler Score
MSIS: Mean Scaled Interval Score

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)

# Out-of-sample forecast accuracy on validation set
accuracy(fc, measures = point_measures, byhorizon = TRUE)
#>                 ME       MAE      MSE      RMSE       MPE     MAPE     MASE
#> CV h=1  0.02185523 0.8052604 1.017906 0.8052604  35.66722 221.8293 0.844289
#> CV h=2  0.01698001 1.0245970 1.632225 1.0245970 -32.41324 319.0622 1.075412
#> CV h=3 -0.01246597 1.0183022 1.622138 1.0183022 -17.90026 271.4276 1.067876
#>            RMSSE
#> CV h=1 0.6697150
#> CV h=2 0.8532125
#> CV h=3 0.8477134
accuracy(fc, measures = interval_measures, level = 95, byhorizon = TRUE)
#>        Winkler_95  MSIS_95
#> CV h=1   5.012254 5.296003
#> CV h=2   6.407682 6.768502
#> CV h=3   6.245013 6.565268

# Accuracy of conformal prediction intervals
scpfc <- conformal(fc, method = "scp", ncal = 50, rolling = TRUE)
accuracy(scpfc, measures = interval_measures, level = 95,
         byhorizon = TRUE)
#>        Winkler_95  MSIS_95
#> CV h=1   5.394495 5.789155
#> CV h=2   6.629521 7.129421
#> CV h=3   6.502841 6.963483

# Out-of-sample forecast accuracy on test set
accuracy(fc, x = c(1, 0.5, 0), measures = interval_measures,
         CV = FALSE, level = 95, byhorizon = TRUE)
#>          Winkler_95  MSIS_95
#> Test h=1   4.079088 4.073511
#> Test h=2   5.045214 5.038316
#> Test h=3   5.050806 5.043901