Temporal bottom-up reconciliation

Temporal bottom-up reconciled forecasts at any temporal aggregation level are computed by appropriate aggregation of the high-frequency base forecasts, \(\widehat{\mathbf{x}}^{[1]}\): $$\widetilde{\mathbf{x}} = \mathbf{S}_{te}\widehat{\mathbf{x}}^{[1]},$$ where \(\mathbf{S}_{te}\) is the temporal structural matrix.

Usage

tebu(base, agg_order, tew = "sum", sntz = FALSE, round = FALSE)

Arguments

base

A (\(hm \times 1\)) numeric vector containing the high-frequency base forecasts; \(m\) is the max. temporal aggregation order, and \(h\) is the forecast horizon for the lowest frequency time series.

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 \(m\).

tew

A string specifying the type of temporal aggregation. Options include: "sum" (simple summation, default), "avg" (average), "first" (first value of the period), and "last" (last value of the period).

sntz

Logical. If TRUE, the negative base forecasts are set to zero (Di Fonzo and Girolimetto, 2023) before applying bottom-up. Default is FALSE.

round

Logical. If TRUE, base forecasts are rounded before applying the bottom-up reconciliation. Default is FALSE.

Value

A (\(h(k^\ast+m) \times 1\)) numeric vector of temporal reconciled forecasts.

References

Di Fonzo, T. and Girolimetto, D. (2023), Spatio-temporal reconciliation of solar forecasts, Solar Energy, 251, 13–29. doi:10.1016/j.solener.2023.01.003

See also

Bottom-up reconciliation: csbu(), ctbu()

Temporal framework: teboot(), tecov(), tegauss(), telcc(), temo(), terec(), tesample(), tetd(), tetools()

Examples

set.seed(123)
# (4 x 1) high frequency base forecasts vector (simulated),
# agg_order = 4 (annual-quarterly)
hfts <- rnorm(4, 5)

reco <- tebu(base = hfts, agg_order = 4)

# Non negative reconciliation
hfts[4] <- -hfts[4] # Making negative one of the quarterly base forecasts
nnreco <- tebu(base = hfts, agg_order = 4, sntz = TRUE)