cssmp: Cross-sectional probabilistic reconciliation (sample...

In FoReco: Forecast Reconciliation

Cross-sectional probabilistic reconciliation (sample approach)

Description

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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)

# Optimal cross-sectional probabilistic reconciliation
reco_dist_opt <- cssmp(base_sample, agg_mat = A)

FoReco documentation built on March 12, 2026, 5:07 p.m.