Some useful tools for the cross-sectional forecast reconciliation of a linearly constrained (e.g., hierarchical/grouped) multiple time series.
hts_tools(C, h = 1, Ut, nb, sparse = TRUE)(\(n_a \times n_b\)) cross-sectional (contemporaneous) matrix mapping the bottom level series into the higher level ones.
Forecast horizon (default is 1).
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
(\(n_a \times n\)).
Number of bottom time series; if C is present, nb
and Ut are not used.
Option to return sparse matrices (default is TRUE).
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 \(\mathbf{U}' = [\mathbf{I} \ -\mathbf{C}]\)
nNumber of variables \(n_a + n_b\).
naNumber of upper level variables.
nbNumber of bottom level variables.
Other utilities:
Cmatrix(),
FoReco2ts(),
agg_ts(),
arrange_hres(),
commat(),
ctf_tools(),
lcmat(),
oct_bounds(),
residuals_matrix(),
score_index(),
shrink_estim(),
thf_tools()