ctmatrix_layouts: Convert between horizon-stacked and cross-temporal layouts

In FoReco: Forecast Reconciliation

Convert between horizon-stacked and cross-temporal layouts

Description

These functions convert matrix between the two canonical layouts used in cross-temporal reconciliation. Let m be the maximum temporal aggregation order and k^\ast the sum of a subset of the (p-1) proper factors of m (excluding m); let h be the forecast horizon for the lowest frequency series (e.g., most aggregated temporal forecast horizon) and n the number of variables:

• Horizon-stacked layout (cross-temporal version): a h \times n(k^\ast + m) matrix where rows are the most aggregated temporal forecast horizons, and the values in each row are ordered from the lowest frequency (most temporally aggregated) to the highest frequency grouped by variable.

• Cross-temporal layout: a n \times h(k^\ast + m) matrix where rows are variables, and horizons for each temporal block appear consecutively. rows are variables, and the values in each row are ordered from the lowest frequency (most temporally aggregated) to the highest frequency.

Then, as_ctmatrix converts a (h \times n(k^\ast+m)) horizon-stacked to a (n \times h(k^\ast+m)) cross-temporal matrix; as_hstack_ctlayout performs the inverse transform.

Usage

as_ctmatrix(hmat, agg_order, n, row_names = NULL)

as_hstack_ctlayout(ctmat, agg_order)

Arguments

hmat	A h \times n(k^\ast+m) numeric matrix in horizon-stacked layout (cross-temporal version).
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.
n	Cross-sectional number of variables.
row_names	Optional character vector of length n with row names for the cross-temporal output of as_ctmatrix(). If NULL (default) no custom names are assigned.
ctmat	A n \times h(k^\ast+m) numeric matrix in cross-temporal layout.

Value

as_ctmatrix returns a n \times h(k^\ast+m) numeric matrix in cross-temporal layout.

as_hstack_ctlayout returns a h \times n(k^\ast+m) numeric matrix in horizon-stacked layout (cross-temporal version).

See Also

Utilities: FoReco2matrix(), aggts(), as_tevector(), balance_hierarchy(), commat(), csprojmat(), cstools(), ctprojmat(), cttools(), df2aggmat(), lcmat(), recoinfo(), res2matrix(), set_bounds(), shrink_estim(), shrink_oasd(), teprojmat(), tetools(), unbalance_hierarchy()

Examples

h <- 2   # horizons
n <- 3   # variables
m <- 4   # temporal aggregation order
kt <- tetools(m)$dim["kt"]

# Build a horizon-stacked matrix: h rows, n * k_t columns
input_ct <- matrix(seq_len(h * n * kt), nrow = n, byrow = TRUE)

hmat <- as_hstack_ctlayout(input_ct, agg_order = m)
ctmat <- as_ctmatrix(hmat, agg_order = m, n = n)
# all.equal(ctmat, input_ct, check.attributes = FALSE)

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