cttd function

Cross-temporal top-down reconciliation

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.

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.

Returns

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

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)

See Also

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

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