Cross-sectional Joint Block Bootstrap

Joint block bootstrap for generating probabilistic base forecasts that take into account the correlation between different time series (Panagiotelis et al. 2023).

Usage

csboot(model_list, boot_size, block_size, seed = NULL, xreg = NULL, ...)

Arguments

model_list

A list of all the \(n\) base forecasts models. 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.

block_size

Block size of the bootstrap, which is typically equivalent to the forecast horizon.

seed

An integer seed.

xreg

An optional 3-d numeric array of dimensions (\(\text{block\_size} \times n \times N_{xreg}\)) containing the new values of xreg to be used for forecasting. It can contain NAs.

...

Additional arguments for the simulate() function.

Value

A list with two elements: the seed used to sample the errors and a 3-d array (\(\text{block\_size} \times n \times \text{boot\_size}\)).

References

Panagiotelis, A., Gamakumara, P., Athanasopoulos, G. and Hyndman, R.J. (2023), Probabilistic forecast reconciliation: Properties, evaluation and score optimisation, European Journal of Operational Research, 306(2), 693–706. doi:10.1016/j.ejor.2022.07.040

See also

Bootstrap samples: ctboot(), teboot()

Cross-sectional framework: csbu(), cscov(), cslcc(), csmo(), csmvn(), csrec(), cssmp(), cstd(), cstools()

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)]
  }
}

# Hierarchy Z = X + Y: 3 series, 50 in-sample residuals each
n <- 3
res <- matrix(rnorm(50 * n), nrow = 50, ncol = n)

# One model per cross-sectional series
model_list <- lapply(seq_len(n), function(i) simple_model(res[, i]))

# Joint block bootstrap: 100 replicates, forecast horizon h = 4
boot <- csboot(model_list = model_list, boot_size = 100, block_size = 4,
               seed = 1)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'obj' in selecting a method for function 'unname': no applicable method for 'simulate' applied to an object of class "simple_model"