Temporal Joint Block Bootstrap

Joint block bootstrap for generating probabilistic base forecasts that take into account the correlation between different temporal aggregation orders (Girolimetto et al. 2023).

Usage

teboot(model_list, boot_size, agg_order, block_size = 1, seed = NULL,
       xreg = NULL, ...)

Arguments

model_list

A list of all the \(p\) base forecasts models ordered from the lowest frequency (most temporally aggregated) to the highest frequency. A simulate() function for each model has to be available and implemented according to the package forecast, with the following mandatory parameters: object, innov, future, and nsim.

boot_size

The number of bootstrap replicates.

agg_order

Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation, \(m\)), or a vector representing a subset of \(p\) factors of \(m\).

block_size

Block size of the bootstrap, which is typically equivalent to the forecast horizon for the most temporally aggregated series.

seed

An integer seed.

xreg

A (\(\text{block\_size}(k^\ast+m) \times N_{xreg}\)) optional numeric matrix containing the new values of xreg to be used for forecasting ordered from the lowest frequency to the highest frequency. It can contains NAs.

...

Additional arguments for the simulate() function.

Value

A list with two elements: the seed used to sample the errors and a (\(\text{boot\_size}\times (k^\ast+m)\text{block\_size}\)) matrix.

References

Girolimetto, D., Athanasopoulos, G., Di Fonzo, T. and Hyndman, R.J. (2024), Cross-temporal probabilistic forecast reconciliation: Methodological and practical issues. International Journal of Forecasting, 40, 3, 1134-1151. doi:10.1016/j.ijforecast.2023.10.003

See also

Bootstrap samples: csboot(), ctboot()

Temporal framework: tebu(), tecov(), telcc(), temo(), temvn(), terec(), tesmp(), tetd(), tetools()

Examples

set.seed(123)

# Minimal example functions: each "model" stores Gaussian residuals;
# simulate() draws new innovations (innov=NULL) or uses the supplied
# ones (innov given).
simple_model <- function(res) {
  structure(list(residuals = res, sigma = sd(res)), class = "simple_model")
}
simulate.simple_model <- function(object, nsim = 1, innov = NULL,
                                  future = TRUE, ...) {
  if (is.null(innov)) {
    rnorm(nsim, mean = 0, sd = object$sigma)
  } else {
    as.numeric(innov)[seq_len(nsim)]
  }
}

# Temporal hierarchy: annual-quarterly, m = 4
# Aggregation orders k = 4, 2, 1 => k* + m = 1 + 2 + 4 = 7 models,
# ordered from the lowest frequency (annual) to the highest (quarterly).
m <- 4
kset <- c(4, 2, 1)              # k = 4 (annual), 2 (semi), 1 (quarterly)
n_obs_per_k <- 40 / kset        # residuals available at each frequency

model_list <- lapply(seq_along(kset), function(i) {
  simple_model(rnorm(n_obs_per_k[i]))
})

# Joint block bootstrap: 100 replicates, block_size = 1 (one annual step)
boot <- teboot(model_list = model_list, boot_size = 100, agg_order = m,
               block_size = 1, seed = 1)
#> Error in UseMethod("simulate"): no applicable method for 'simulate' applied to an object of class "simple_model"

dim(boot$boot)   # boot_size x (k* + m)*block_size  => 100 x 7
#> Error: object 'boot' not found