FoReco (version 1.0.0)

csmo: Cross-sectional middle-out reconciliation

Description

The middle-out forecast reconciliation (Athanasopoulos et al., 2009) combines top-down (cstd) and bottom-up (csbu) for genuine hierarchical/grouped time series. Given the base forecasts of variables at an intermediate level \(l\), it performs

• a top-down approach for the levels \(<l\);

• a bottom-up approach for the levels \(>l\).

Usage

csmo(base, agg_mat, id_rows = 1, weights, normalize = TRUE)

Value

A (\(h \times n\)) numeric matrix of cross-sectional reconciled forecasts.

Arguments

base

A (\(h \times n_l\)) numeric matrix containing the \(l\)-level base forecast; \(n_l\) is the number of variables at level \(l\), and \(h\) is the forecast horizon.

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.

id_rows

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

weights

A (\(h \times n_b\)) numeric matrix containing the proportions for the bottom time series; \(h\) is the forecast horizon, and \(n_b\) is the total number of bottom variables.

normalize

If TRUE (default), the weights will sum to 1.

References

Athanasopoulos, G., Ahmed, R. A. and Hyndman, R.J. (2009) Hierarchical forecasts for Australian domestic tourism. International Journal of Forecasting 25(1), 146–166. tools:::Rd_expr_doi("10.1016/j.ijforecast.2008.07.004")

See Also

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

Cross-sectional framework: csboot(), csbu(), cscov(), cslcc(), csrec(), cstd(), cstools()

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)
# (3 x 2) top base forecasts vector (simulated), forecast horizon = 3
baseL2 <- matrix(rnorm(2*3, 5), 3, 2)
# Same weights for different forecast horizons
fix_weights <- runif(4)
reco <- csmo(base = baseL2, agg_mat = A, id_rows = 2:3, weights = fix_weights)

# Different weights for different forecast horizons
h_weights <- matrix(runif(4*3), 3, 4)
recoh <- csmo(base = baseL2, agg_mat = A, id_rows = 2:3, weights = h_weights)