FoReco (version 1.0.0)

temo: Temporal middle-out reconciliation

Description

The middle-out forecast reconciliation for temporal hierarchies combines top-down (tetd) and bottom-up (tebu) methods. Given the base forecasts of an intermediate temporal aggregation order \(k\), it performs

• a top-down approach for the aggregation orders \(<k\);

• a bottom-up approach for the aggregation orders \(>k\).

Usage

temo(base, agg_order, order = max(agg_order), weights, tew = "sum",
     normalize = TRUE)

Value

A (\(h(k^\ast+m) \times 1\)) numeric vector of temporal reconciled forecasts.

Arguments

base

A (\(hk \times 1\)) numeric vector containing the temporal aggregated base forecasts of order \(k\); \(k\) is an aggregation order (a factor of \(m\), and \(1<k<m\)), \(m\) is the max aggregation order, and \(h\) is the forecast horizon for the lowest frequency time series.

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 \(m\).

order

The intermediate fixed aggregation order \(k\).

weights

A (\(hm \times 1\)) numeric vector containing the proportions for the high-frequency time series; \(m\) 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

Middle-out reconciliation: csmo(), ctmo()

Temporal framework: teboot(), tebu(), tecov(), telcc(), terec(), tetd(), tetools()

Examples

set.seed(123)
# (6 x 1) base forecasts vector (simulated), forecast horizon = 3
# and intermediate aggregation order k = 2 (max agg order = 4)
basek2 <- rnorm(3*2, 5)
# Same weights for different forecast horizons
fix_weights <- runif(4)
reco <- temo(base = basek2, order = 2, agg_order = 4, weights = fix_weights)

# Different weights for different forecast horizons
h_weights <- runif(4*3)
recoh <- temo(base = basek2, order = 2, agg_order = 4, weights = h_weights)