ctbu function

Cross-temporal bottom-up reconciliation

Cross-temporal bottom-up reconciled forecasts for all series at any temporal aggregation level are computed by appropriate summation of the high-frequency bottom base forecasts $\widehat{\mathbf{B}^{[1]}}$: [REMOVE_ME]$\widetilde{\mathbf{X}} = \mathbf{S}_{cs}\widehat{\mathbf{B}^{[1]}}\mathbf{S}'_{te}, [REMOVE_ME_2]$

where $\mathbf{S}_{cs}$ and $\mathbf{S}_{te}$ are the cross-sectional and temporal structural matrices, respectively.

ctbu(base, agg_mat, agg_order, tew = "sum", sntz = FALSE)

Arguments

• base: A ($n_b \times hm$) numeric matrix containing high-frequency bottom base forecasts; $n_b$ is the total number of high-frequency bottom variables, $m$ is the max aggregation order, and $h$ is the forecast horizon for the lowest frequency time series.
• agg_mat: A ($n_a \times n_b$) numeric matrix representing the cross-sectional aggregation matrix. It maps the $n_b$ bottom-level (free) variables into the $n_a$ upper (constrained) variables.
• 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: If TRUE, the negative base forecasts are set to zero before applying bottom-up.

Returns

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

Description

Cross-temporal bottom-up reconciled forecasts for all series at any temporal aggregation level are computed by appropriate summation of the high-frequency bottom base forecasts $\widehat{\mathbf{B}^{[1]}}$:

where $\mathbf{S}_{cs}$ and $\mathbf{S}_{te}$ are the cross-sectional and temporal structural matrices, respectively.

Examples

set.seed(123)
# Aggregation matrix for Z = X + Y
A <- t(c(1,1))
# (2 x 4) high frequency bottom base forecasts matrix (simulated),
# agg_order = 4 (annual-quarterly)
hfbts <- matrix(rnorm(4*2, 2.5), 2, 4)

reco <- ctbu(base = hfbts, agg_mat = A, agg_order = 4)

# Non negative reconciliation
hfbts[1,4] <- -hfbts[1,4] # Making negative one of the quarterly base forecasts for variable X
nnreco <- ctbu(base = hfbts, agg_mat = A, agg_order = 4, sntz = TRUE)

See Also

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

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