FoReco (version 1.0.0)

cttd: Cross-temporal top-down reconciliation

Description

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)

Value

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

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.

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)