FoReco (version 1.0.0)

ctmo: Cross-temporal middle-out reconciliation

Description

The cross-temporal middle-out forecast reconciliation combines top-down (cttd) and bottom-up (ctbu) methods in the cross-temporal framework for genuine hierarchical/grouped time series. Given the base forecasts of an intermediate cross-sectional level \(l\) and aggregation order \(k\), it performs

• a top-down approach for the aggregation orders \(\geq k\) and cross-sectional levels \(\geq l\);

• a bottom-up approach, otherwise.

Usage

ctmo(base, agg_mat, agg_order, id_rows = 1, order = max(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 (\(n_l \times hk\)) numeric matrix containing the \(l\)-level base forecasts of temporal aggregation order \(k\); \(n_l\) is the number of variables at level \(l\), \(k\) 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_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 \(m\).

id_rows

A numeric vector indicating the \(l\)-level rows of agg_mat.

order

The intermediate fixed aggregation order \(k\).

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

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

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

Examples

set.seed(123)
# Aggregation matrix for Z = X + Y, X = XX + XY and Y = YX + YY
A <- matrix(c(1,1,1,1,1,1,0,0,0,0,1,1), 3, byrow = TRUE)
# (2 x 6) base forecasts matrix (simulated), forecast horizon = 3
# and intermediate aggregation order k = 2 (max agg order = 4)
baseL2k2 <- rbind(rnorm(3*2, 5), rnorm(3*2, 5))

# Same weights for different forecast horizons, agg_order = 4
fix_weights <- matrix(runif(4*4), 4, 4)
reco <- ctmo(base = baseL2k2, id_rows = 2:3, agg_mat = A,
             order = 2, agg_order = 4, weights = fix_weights)

# Different weights for different forecast horizons
h_weights <- matrix(runif(4*4*3), 4, 3*4)
recoh <- ctmo(base = baseL2k2, id_rows = 2:3, agg_mat = A,
             order = 2, agg_order = 4, weights = h_weights)