hts_tools {FoReco}

Cross-sectional reconciliation tools

Description

Some useful tools for the cross-sectional forecast reconciliation of a linearly constrained (e.g., hierarchical/grouped) multiple time series.

Usage

hts_tools(C, h = 1, Ut, nb, sparse = TRUE)

Arguments

C

(\(n_a \times n_b\)) cross-sectional (contemporaneous) matrix mapping the bottom level series into the higher level ones.

h

Forecast horizon (default is 1).

Ut

Zero constraints cross-sectional (contemporaneous) kernel matrix \((\mathbf{U}'\mathbf{y} = \mathbf{0})\) spanning the null space valid for the reconciled forecasts. It can be used instead of parameter C, but nb is needed if \(\mathbf{U}' \neq [\mathbf{I} \ -\mathbf{C}]\). If the hierarchy admits a structural representation, \(\mathbf{U}'\) has dimension (\(n_a \times n\)).

nb

Number of bottom time series; if C is present, nb and Ut are not used.

sparse

Option to return sparse matrices (default is TRUE).

Value

A list of five elements:

C

(\(n \times n_b\)) cross-sectional (contemporaneous) aggregation matrix.

S

(\(n \times n_b\)) cross-sectional (contemporaneous) summing matrix, \(\mathbf{S} = \left[\begin{array}{c} \mathbf{C} \cr \mathbf{I}_{n_b}\end{array}\right].\)

Ut

(\(n_a \times n\)) zero constraints cross-sectional (contemporaneous) kernel matrix. If the hierarchy admits a structural representation \(\mathbf{U}' = [\mathbf{I} \ -\mathbf{C}]\)

n

Number of variables \(n_a + n_b\).

na

Number of upper level variables.

nb

Number of bottom level variables.

See Also

Other utilities: Cmatrix(), FoReco2ts(), agg_ts(), arrange_hres(), commat(), ctf_tools(), lcmat(), oct_bounds(), residuals_matrix(), score_index(), shrink_estim(), thf_tools()

Examples

# One level hierarchy (na = 1, nb = 2)
obj <- hts_tools(C = matrix(c(1, 1), 1), sparse = FALSE)