The R package conformalForecast provides methods and tools for performing multistep-ahead time series forecasting using conformal prediction methods including classical conformal prediction, adaptive conformal prediction, conformal PID control, and autocorrelated multistep-ahead conformal prediction.
Installation
You can install the development version of conformalForecast from GitHub with:
# install.packages("remotes")
remotes::install_github("xqnwang/conformalForecast")You can also get the official release version from CRAN with:
install.packages("conformalForecast")Example
This basic example shows how to perform classical conformal prediction and update the results when new observations become available.
We simulate a series from an AR(2) model, holding back the last five observations to stand in for data that arrives later:
library(conformalForecast)
set.seed(0)
series_all <- arima.sim(n = 1005, list(ar = c(0.8, -0.5)), sd = 1)
series <- head(series_all, 1000)
new_data <- as.numeric(tail(series_all, 5))Conformal calibration needs a record of past forecast errors. We obtain one with cvforecast(), which refits the model on a rolling forecast origin and stores the out-of-sample errors at every horizon:
far2 <- function(x, h, level) {
Arima(x, order = c(2, 0, 0)) |>
forecast(h = h, level = level)
}
fc <- cvforecast(series, forecastfun = far2, h = 3, level = c(80, 95),
forward = TRUE, initial = 1, window = 100)For a base model that returns only point forecasts, use level = NULL in cvforecast() and supply alpha explicitly when calibrating (for example, alpha = 0.1 for 90% conformal intervals).
Now calibrate intervals with split conformal prediction, on a rolling window of 100 calibration scores:
scpfc <- conformal(fc, method = "scp", ncal = 100, rolling = TRUE)When the five held-back observations arrive, update() extends the fit incrementally. Intervals that were already issued do not change:
scpfc_updated <- update(scpfc, new_data = new_data, forecastfun = far2)Finally, evaluate the intervals by forecast horizon:
# Interval forecast accuracy
accuracy(scpfc_updated, byhorizon = TRUE)
#> Winkler_95 MSIS_95
#> CV h=1 5.024650 4.850147
#> CV h=2 6.442104 6.218875
#> CV h=3 6.568085 6.335622
# Mean coverage
coverage(scpfc_updated, level = 95)
#> h=1 h=2 h=3
#> 0.9577640 0.9613948 0.9488140
# Mean and median interval width
width(scpfc_updated, level = 95, includemedian = TRUE)
#> Mean width:
#> h=1 h=2 h=3
#> 4.289693 5.570434 5.607451
#>
#> Median width:
#> h=1 h=2 h=3
#> 4.154276 5.619012 5.404932Learn more
- Introduction to conformalForecast: conformal methods, their formulas and tuning arguments, with a comparison of coverage and interval width.
-
Updating conformal forecasts with new data: how
update()extends a fitted pipeline as observations arrive, and when it is equivalent to refitting.