ctf_tools: Cross-temporal reconciliation tools

View source: R/ctf_tools.R

ctf_toolsR Documentation

Cross-temporal reconciliation tools

Description

\loadmathjax

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

Usage

ctf_tools(C, m, h = 1, Ut, nb, sparse = TRUE)

Arguments

C

(\mjseqnn_a \times n_b) 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, \mjseqnm), or a subset of the \mjseqnp factors of \mjseqnm.

h

Forecast horizon for the lowest frequency (most temporally aggregated) time series (default is 1).

Ut

Zero constraints cross-sectional (contemporaneous) kernel matrix \mjseqn(\mathbfU'\mathbfy = \mathbf0) spanning the null space valid for the reconciled forecasts. It can be used instead of parameter C, but nb (\mjseqnn = n_a + n_b) is needed if \mjseqn\mathbfU' \neq [\mathbfI \ -\mathbfC]. If the hierarchy admits a structural representation, \mjseqn\mathbfU' has dimension (\mjseqnn_a \times n).

nb

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

sparse

Option to return sparse object (default is TRUE).

Value

ctf list with:

Ht

Full row-rank cross-temporal zero constraints (kernel) matrix coherent with \mjseqn\mathbfy = \mboxvec(\mathbfY'): \mjseqn\mathbfH'\mathbfy = \mathbf0.

Hbrevet

Complete, not full row-rank cross-temporal zero constraints (kernel) matrix coherent with \mjseqn\mathbfy = \mboxvec(\mathbfY'): \mjseqn\breve\mathbfH'\mathbfy = \mathbf0.

Hcheckt

Full row-rank cross-temporal zero constraints (kernel) matrix coherent with \mjseqn\check\mathbfy (structural representation): \mjseqn\check\mathbfH' \check\mathbfy = \mathbf0.

Ccheck

Cross-temporal aggregation matrix \mjseqn\check\mathbfC coherent with \mjseqn\check\mathbfy (structural representation).

Scheck

Cross-temporal summing matrix \mjseqn\check\mathbfS coherent with \mjseqn\check\mathbfy (structural representation).

Fmat

Cross-temporal summing matrix \mjseqn\widetilde\mathbfF coherent with \mjseqn\mathbfy = \mboxvec(\mathbfY').

hts list from hts_tools .

thf list from thf_tools .

See Also

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

Examples

# One level hierarchy (na = 1, nb = 2) with quarterly data
obj <- ctf_tools(C = matrix(c(1, 1), 1), m = 4)


FoReco documentation built on May 31, 2023, 5:17 p.m.