Cross-sectional probabilistic reconciliation (sample approach)

This function performs cross-sectional probabilistic forecast reconciliation using a sample-based approach (Panagiotelis et al., 2023, Girolimetto et al., 2024) for linearly constrained (e.g., hierarchical or grouped) multiple time series. Given an array of \(L\) simulated base forecast draws, cssmp() applies a chosen FoReco reconciliation independently to each draw, producing a coherent sample distribution of reconciled forecasts. Typical choices for the reconciliation include optimal combination (csrec) as well as top-down (cstd), middle-out (csmo), bottom-up (csbu), and level-conditional (cslcc) approaches.

Usage

cssmp(sample, fun = csrec, ...)

Arguments

sample

A (\(h \times n \times L\)) numeric array containing the base forecasts samples to be reconciled; \(h\) is the forecast horizon, \(n\) is the total number of time series (\(n = n_a + n_b\)), and \(L\) is the sample size.

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

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

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

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

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

Examples

set.seed(123)
A <- matrix(c(1,1,1,1,  # Z = X + Y
              1,1,0,0,  # X = XX + XY
              0,0,1,1), # Y = YX + YY
              nrow = 3, byrow = TRUE)
rownames(A) <- c("Z", "X", "Y")
colnames(A) <- c("XX", "XY", "YX", "YY")

# (100 x 7) base forecasts sample (simulated) for h = 1
base_h1 <- matrix(rnorm(100*7, mean = c(20, rep(10, 2), rep(5, 4))),
                  100, byrow = TRUE)
# (100 x 7) base forecasts sample (simulated) for h = 2
base_h2 <- matrix(rnorm(100*7, mean = c(20, rep(10, 2), rep(5, 4))),
                  100, byrow = TRUE)
# (2 x 7 x 100) base forecasts sample array with
# 2 forecast horizons, 7 time series and 100 sample
base_sample <- aperm(simplify2array(list(base_h1, base_h2)), c(3,2,1))

# Top-down probabilistic reconciliation
reco_dist_td <- cssmp(base_sample[, 1, , drop = FALSE], agg_mat = A,
                      fun = cstd, weights = c(0.3, 0.2, 0.1, 0.4))

# Middle-out probabilistic reconciliation
reco_dist_mo <- cssmp(base_sample[, c(2,3), , drop = FALSE], agg_mat = A,
                      fun = csmo, weights = c(0.3, 0.7, 0.8, 0.2),
                      id_rows = 2:3)

# Bottom-up probabilistic reconciliation
reco_dist_bu <- cssmp(base_sample[,-c(1:3),], agg_mat = A, fun = csbu)

# Level conditional coherent probabilistic reconciliation
reco_dist_lcc <- cssmp(base_sample, agg_mat = A, fun = cslcc)
#> Warning: Argument `res` is ignored.
#> ℹ When `res` is provided, `comb = 'shr'` is suggested.

# Optimal cross-sectional probabilistic reconciliation
reco_dist_opt <- cssmp(base_sample, agg_mat = A)
#> Warning: Argument `res` is ignored.
#> ℹ When `res` is provided, `comb = 'shr'` is suggested.