csbu: Cross-sectional bottom-up reconciliation

Description

This function computes the cross-sectional bottom-up reconciled forecasts (Dunn et al., 1976) for all series by appropriate summation of the bottom base forecasts $\widehat{\mathbf{b}}$: $$\widetilde{\mathbf{y}} = \mathbf{S}_{cs}\widehat{\mathbf{b}},$$ where $\mathbf{S}_{cs}$ is the cross-sectional structural matrix.

Usage

csbu(base, agg_mat, sntz = FALSE)

Value

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

Arguments

base: A ($h \times n_b$) numeric matrix or multivariate time series (mts class) containing bottom base forecasts; $h$ is the forecast horizon, and $n_b$ is the total number of bottom variables.
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.
sntz: If TRUE, the negative base forecasts are set to zero before applying bottom-up.

References

Dunn, D. M., Williams, W. H. and Dechaine, T. L. (1976), Aggregate versus subaggregate models in local area forecasting, Journal of the American Statistical Association 71(353), 68–71. tools:::Rd_expr_doi("10.1080/01621459.1976.10481478")

Examples

Run this code

set.seed(123)
# (3 x 2) bottom base forecasts matrix (simulated), Z = X + Y
bts <- matrix(rnorm(6, mean = c(10, 10)), 3, byrow = TRUE)

# Aggregation matrix for Z = X + Y
A <- t(c(1,1))
reco <- csbu(base = bts, agg_mat = A)

# Non negative reconciliation
bts[2,2] <- -bts[2,2] # Making negative one of the base forecasts for variable Y
nnreco <- csbu(base = bts, agg_mat = A, sntz = TRUE)