ctmo: Cross-temporal middle-out reconciliation

In FoReco: Forecast Reconciliation

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)

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.

Value

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

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)

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