Temporal probabilistic reconciliation (sample approach)

This function performs temporal probabilistic forecast reconciliation using a sample-based approach (Girolimetto et al., 2024) for a single time series using temporal hierarchies (Athanasopoulos et al., 2017). Given a \((L \times h(k^\ast + m))\) matrix of simulated base forecast draws, tesmp() applies a chosen FoReco temporal reconciliation independently to each draw, producing a coherent sample distribution of reconciled forecasts across the temporal hierarchy. Typical choices for the reconciliation include optimal combination (terec) as well as top-down (tetd), middle-out (temo), bottom-up (tebu), and level-conditional (telcc) approaches.

Usage

tesmp(sample, agg_order, fun = terec, ...)

Arguments

sample

A (\(L \times h(k^\ast + m)\)) numeric matrix containing the base forecasts samples to be reconciled; \(m\) is the max aggregation order, \(k^\ast\) is the sum of (a subset of) (\(p-1\)) factors of \(m\), excluding \(m\), \(h\) is the forecast horizon for the lowest frequency time series, and \(L\) is the sample size.

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 \(m\).

fun

A string specifying the reconciliation function to be used, as implemented in FoReco.

...

Arguments passed on to fun

Value

A distributional::dist_sample object.

References

Athanasopoulos, G., Hyndman, R.J., Kourentzes, N. and Petropoulos, F. (2017), Forecasting with Temporal Hierarchies, European Journal of Operational Research, 262, 1, 60-74. doi:10.1016/j.ejor.2017.02.046

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

Probabilistic reconciliation: csmvn(), cssmp(), ctmvn(), ctsmp(), temvn()

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

Examples

set.seed(123)
m <- 4 # from quarterly to annual temporal aggregation

# (100 x 14) base forecasts sample matrix (simulated), m = 4, h = 2
sample <- t(sapply(1:100, function(x) {
  rnorm(14, rep(c(20, 10, 5), 2 * c(1, 2, 4)))
}))
# (70 x 1) in-sample residuals vector (simulated)
res <- rnorm(70)

# Top-down probabilistic reconciliation
reco_dist_td <- tesmp(sample[,c(1:2), drop = FALSE], agg_order = m,
                      fun = tetd, weights = c(0.2, 0.5, 0.3, 0.3))

# Middle-out probabilistic reconciliation
tesmp(sample[,c(3:6), drop = FALSE], agg_order = m,
      fun = temo, weights = c(0.2, 0.5, 0.3, 0.3), order = 2)
#> <distribution[2]>
#>       tao-1       tao-2 
#> sample[100] sample[100] 

# Bottom-up probabilistic reconciliation
reco_dist_bu <- tesmp(sample[,-c(1:6)], agg_order = m, fun = tebu)

# Level conditional coherent probabilistic reconciliation
reco_dist_lcc <- tesmp(sample, agg_order = m, fun = telcc)
#> Warning: Argument `res` is ignored.
#> ℹ When `res` is provided, `comb = 'wlsv'` is suggested.

# Optimal cross-sectional probabilistic reconciliation
reco_dist_opt <- tesmp(sample, agg_order = m, res = res, comb = "wlsv")