cttd: Cross-temporal top-down reconciliation

In FoReco: Forecast Reconciliation

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)

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)

FoReco documentation built on Sept. 14, 2024, 9:07 a.m.