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

## Arguments

- model_list
A list of \(n\) elements, one for each cross-sectional series. Each elements is a list with the \((k^\ast+m)\) 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.

## Value

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

## References

Girolimetto, D., Athanasopoulos, G., Di Fonzo, T. and Hyndman, R.J. (2023), Cross-temporal
probabilistic forecast reconciliation: Methodological and practical issues.
*International Journal of Forecasting*, in press. doi:10.1016/j.ijforecast.2023.10.003