FoReco (version 1.0.0)

tcsrec: Heuristic cross-temporal reconciliation

Description

tcsrec replicates the procedure by Kourentzes and Athanasopoulos (2019): (i) for each time series the forecasts at any temporal aggregation order are reconciled using temporal hierarchies; (ii) time-by-time cross-sectional reconciliation is performed; and (iii) the projection matrices obtained at step (ii) are then averaged and used to cross-sectionally reconcile the forecasts obtained at step (i). In cstrec, the order of application of the two reconciliation steps (temporal first, then cross-sectional), is inverted compared to tcsrec (Di Fonzo and Girolimetto, 2023).

Usage

# First-temporal-then-cross-sectional forecast reconciliation
tcsrec(base, cslist, telist, res = NULL, avg = "KA")
# First-cross-sectional-then-temporal forecast reconciliation
cstrec(base, cslist, telist, res = NULL)

Value

A (\(n \times h(k^\ast+m)\)) numeric matrix of cross-temporal reconciled forecasts.

Arguments

base

A (\(n \times h(k^\ast+m)\)) numeric matrix containing the base forecasts to be reconciled; \(n\) is the total number of variables, \(m\) is the max. order of temporal aggregation, \(k^\ast\) is the sum of (a subset of) (\(p-1\)) factors of \(m\), excluding \(m\), and \(h\) is the forecast horizon for the lowest frequency time series. The row identifies a time series, and the forecasts in each row are ordered from the lowest frequency (most temporally aggregated) to the highest frequency.

cslist

A list of elements for the cross-sectional reconciliation. See csrec for a complete list (excluded base and res).

telist

A list of elements for the temporal reconciliation. See terec for a complete list (excluded base and res).

res

A (\(n \times N(k^\ast+m)\)) optional numeric matrix containing the in-sample residuals at all the temporal frequencies ordered from the lowest frequency to the highest frequency (columns) for each variable (rows). This matrix is used to compute some covariance matrices.

avg

If avg = "KA" (default), the final projection matrix \(\mathbf{M}\) is the one proposed by Kourentzes and Athanasopoulos (2019), otherwise it is calculated as simple average of all the involved projection matrices at step 2 of the procedure (see Di Fonzo and Girolimetto, 2023).

Warning

The two-step heuristic reconciliation allows considering non negativity constraints only in the first step. This means that non-negativity is not guaranteed in the final reconciled values.

References

Di Fonzo, T. and Girolimetto, D. (2023), Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives, International Journal of Forecasting, 39, 1, 39-57. tools:::Rd_expr_doi("10.1016/j.ijforecast.2021.08.004")

Kourentzes, N. and Athanasopoulos, G. (2019), Cross-temporal coherent forecasts for Australian tourism, Annals of Tourism Research, 75, 393-409. tools:::Rd_expr_doi("10.1016/j.annals.2019.02.001")

See Also

Cross-temporal framework: ctboot(), ctbu(), ctcov(), ctlcc(), ctmo(), ctrec(), cttd(), cttools(), iterec()

Examples

set.seed(123)
# (3 x 7) base forecasts matrix (simulated), Z = X + Y and m = 4
base <- rbind(rnorm(7, rep(c(20, 10, 5), c(1, 2, 4))),
              rnorm(7, rep(c(10, 5, 2.5), c(1, 2, 4))),
              rnorm(7, rep(c(10, 5, 2.5), c(1, 2, 4))))
# (3 x 70) in-sample residuals matrix (simulated)
res <- rbind(rnorm(70), rnorm(70), rnorm(70))

A <- t(c(1,1)) # Aggregation matrix for Z = X + Y
m <- 4 # from quarterly to annual temporal aggregation

rtcs <- tcsrec(base = base,
               cslist = list(agg_mat = A, comb = "shr"),
               telist = list(agg_order = m, comb = "wlsv"),
               res = res)

rcst <- tcsrec(base = base,
               cslist = list(agg_mat = A, comb = "shr"),
               telist = list(agg_order = m, comb = "wlsv"),
               res = res)