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