csmo function

Cross-sectional middle-out reconciliation

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 $\>l$.

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

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.

Returns

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

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)

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()