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Cross-temporal top-down reconciliation

Source: R/topdown.R
cttd.Rd

Top-down forecast reconciliation for cross-temporal hierarchical/grouped time series, where the forecast of a `Total' (top-level series, expected to be positive) is disaggregated according to a proportional scheme (weights). Besides fulfilling any aggregation constraint, the top-down reconciled forecasts should respect two main properties:

  • the top-level value remains unchanged;

  • all the bottom time series reconciled forecasts are non-negative.

Usage

cttd(base, agg_mat, agg_order, weights, tew = "sum", normalize = TRUE)

Arguments

base

A (\(hm \times 1\)) numeric vector containing top- and \(m\) temporal aggregated level base forecasts; \(m\) 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 \(m\).

weights

A (\(n_b \times hm\)) numeric matrix containing the proportions for each high-frequency bottom time series; \(n_b\) 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.

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).

normalize

If TRUE (default), the weights will sum to 1.

Value

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

See also

Top-down reconciliation: cstd(), tetd()

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

Examples

set.seed(123)
# (3 x 1) top base forecasts vector (simulated), forecast horizon = 3
topf <- rnorm(3, 10)
A <- t(c(1,1)) # Aggregation matrix for Z = X + Y

# Same weights for different forecast horizons, agg_order = 4
fix_weights <- matrix(runif(4*2), 2, 4)
reco <- cttd(base = topf, agg_mat = A, agg_order = 4, weights = fix_weights)

# Different weights for different forecast horizons
h_weights <- matrix(runif(4*2*3), 2, 3*4)
recoh <- cttd(base = topf, agg_mat = A, agg_order = 4, weights = h_weights)