Some useful tools for the cross-temporal forecast reconciliation of cross-sectionally and
temporally constrained time series
Usage
ctf_tools(C, m, h = 1, Ut, nb, Sstruc = FALSE)
Arguments
C
(na x nb) cross-sectional (contemporaneous) matrix mapping the bottom
level series into the higher level ones.
m
Highest available sampling frequency per seasonal cycle (max. order of
temporal aggregation).
h
Forecast horizon for the lowest frequency (most temporally aggregated) time
series (default is 1).
Ut
Zero constraints cross-sectional (contemporaneous) kernel matrix
\((\textbf{U}'\textbf{Y} = \mathbf{0})\) spanning the null space valid for the reconciled
forecasts. It can be used instead of parameter C, but in this case nb (n = na + nb) is needed. If
the hierarchy admits a structural representation, Ut has dimension (na x n).
nb
Number of bottom time series; if C is present, nb is not used.
Sstruc
If Sstruc = TRUE the function returns also the structural representation matrix of
a cross-temporal system (default is FALSE).
Value
ctf list with:
Ht
Full row-rank cross-temporal zero-valued constraints (kernel)
matrix\(,\; \textbf{H}'\textbf{y} = \mathbf{0}\).
Htbreve
Complete, not full row-rank cross-temporal zero-valued
constraints (kernel) matrix.
Htstruc
Zero constraints full row-rank cross-temporal kernel matrix
(structural representation) \(,\; \check{\textbf{H}}'\).