Some useful tools for the cross-temporal forecast reconciliation of a linearly constrained (e.g., hierarchical/grouped) multiple time series.
Arguments
- 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.
- cons_mat
A (\(n_a \times n\)) numeric matrix representing the cross-sectional zero constraints: each row represents a constraint equation, and each column represents a variable. The matrix can be of full rank, meaning the rows are linearly independent, but this is not a strict requirement, as the function allows for redundancy in the constraints.
- agg_order
Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation, \(m\)), or a vector representing a subset of \(p\) factors of \(m\).
- tew
A string specifying the type of temporal aggregation. Options include: "
sum" (simple summation, default), "avg" (average), "first" (first value of the period), and "last" (last value of the period).- fh
Forecast horizon for the lowest frequency (most temporally aggregated) time series (default is
1).- sparse
Option to return sparse matrices (default is
TRUE).
Value
A list with four elements:
- dim
A vector containing information about the number of series for the complete system (
n), for upper levels (na) and bottom level (nb), the maximum aggregation order (m), the number of factor (p), the partial (ks) and total sum (kt) of factors.- set
The vector of the temporal aggregation orders (in decreasing order).
- agg_mat
The cross-temporal aggregation matrix.
- strc_mat
The cross-temporal structural matrix.
- cons_mat
The cross-temporal zero constraints matrix.
See also
Cross-temporal framework:
ctboot(),
ctbu(),
ctcov(),
ctlcc(),
ctmo(),
ctrec(),
cttd(),
iterec(),
tcsrec()
Utilities:
FoReco2matrix(),
aggts(),
balance_hierarchy(),
commat(),
csprojmat(),
cstools(),
ctprojmat(),
df2aggmat(),
lcmat(),
recoinfo(),
res2matrix(),
set_bounds(),
shrink_estim(),
shrink_oasd(),
teprojmat(),
tetools(),
unbalance_hierarchy()
Examples
# Cross-temporal framework
A <- t(c(1,1)) # Aggregation matrix for Z = X + Y
m <- 4 # from quarterly to annual temporal aggregation
cttools(agg_mat = A, agg_order = m)
#> $dim
#> n na nb m p ks kt
#> 3 1 2 4 3 3 7
#>
#> $set
#> [1] 4 2 1
#>
#> $agg_mat
#> 13 x 8 sparse Matrix of class "dgCMatrix"
#>
#> [1,] 1 1 1 1 1 1 1 1
#> [2,] 1 1 . . 1 1 . .
#> [3,] . . 1 1 . . 1 1
#> [4,] 1 . . . 1 . . .
#> [5,] . 1 . . . 1 . .
#> [6,] . . 1 . . . 1 .
#> [7,] . . . 1 . . . 1
#> [8,] 1 1 1 1 . . . .
#> [9,] 1 1 . . . . . .
#> [10,] . . 1 1 . . . .
#> [11,] . . . . 1 1 1 1
#> [12,] . . . . 1 1 . .
#> [13,] . . . . . . 1 1
#>
#> $strc_mat
#> 21 x 8 sparse Matrix of class "dgCMatrix"
#>
#> [1,] 1 1 1 1 1 1 1 1
#> [2,] 1 1 . . 1 1 . .
#> [3,] . . 1 1 . . 1 1
#> [4,] 1 . . . 1 . . .
#> [5,] . 1 . . . 1 . .
#> [6,] . . 1 . . . 1 .
#> [7,] . . . 1 . . . 1
#> [8,] 1 1 1 1 . . . .
#> [9,] 1 1 . . . . . .
#> [10,] . . 1 1 . . . .
#> [11,] 1 . . . . . . .
#> [12,] . 1 . . . . . .
#> [13,] . . 1 . . . . .
#> [14,] . . . 1 . . . .
#> [15,] . . . . 1 1 1 1
#> [16,] . . . . 1 1 . .
#> [17,] . . . . . . 1 1
#> [18,] . . . . 1 . . .
#> [19,] . . . . . 1 . .
#> [20,] . . . . . . 1 .
#> [21,] . . . . . . . 1
#>
#> $cons_mat
#> 13 x 21 sparse Matrix of class "dgCMatrix"
#>
#> [1,] . . . 1 . . . . . . -1 . . . . . . -1 . . .
#> [2,] . . . . 1 . . . . . . -1 . . . . . . -1 . .
#> [3,] . . . . . 1 . . . . . . -1 . . . . . . -1 .
#> [4,] . . . . . . 1 . . . . . . -1 . . . . . . -1
#> [5,] 1 . . -1 -1 -1 -1 . . . . . . . . . . . . . .
#> [6,] . 1 . -1 -1 . . . . . . . . . . . . . . . .
#> [7,] . . 1 . . -1 -1 . . . . . . . . . . . . . .
#> [8,] . . . . . . . 1 . . -1 -1 -1 -1 . . . . . . .
#> [9,] . . . . . . . . 1 . -1 -1 . . . . . . . . .
#> [10,] . . . . . . . . . 1 . . -1 -1 . . . . . . .
#> [11,] . . . . . . . . . . . . . . 1 . . -1 -1 -1 -1
#> [12,] . . . . . . . . . . . . . . . 1 . -1 -1 . .
#> [13,] . . . . . . . . . . . . . . . . 1 . . -1 -1
#>