balance_hierarchy function

Aggregation matrix of a (possibly) unbalanced hierarchy in balanced form

A hierarchy with $L$ upper levels is said to be balanced if each variable at level $l$ has at least one child at level $l+1$. When this doesn't hold, the hierarchy is unbalanced. This function transforms an aggregation matrix of an unbalanced hierarchy into an aggregation matrix of a balanced one. This function is used to reconcile forecasts with cslcc , which operates exclusively with balanced hierarchies.

balance_hierarchy(agg_mat, nodes = "auto", sparse = TRUE)

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.

• nodes: A ($L \times 1$) numeric vector indicating the number of variables in each of the upper $L$ levels of the hierarchy. The default

  value is the string "auto" which calculates the number of variables in each level.

• sparse: Option to return sparse matrices (default is TRUE).

Returns

A list containing four elements: - bam: The balanced aggregation matrix.

• agg_mat: The input matrix.

• nodes: A ($L \times 1$) numeric vector indicating the number of variables in each of the $L$ upper levels of the balanced hierarchy.

• id: The identification number of each variable in the balanced hierarchy. It may contains duplicated values.

Examples

#    Unbalanced     ->      Balanced
#        T                     T
#    |-------|             |-------|
#    A       |             A       B
#  |---|     |           |---|     |
# AA   AB    B          AA   AB    BA
A <- matrix(c(1, 1, 1,
              1, 1, 0), 2, byrow = TRUE)
obj <- balance_hierarchy(agg_mat = A, nodes = c(1, 1))
obj$bam

See Also

Utilities: FoReco2matrix(), aggts(), commat(), csprojmat(), cstools(), ctprojmat(), cttools(), df2aggmat(), lcmat(), recoinfo(), res2matrix(), shrink_estim(), teprojmat(), tetools(), unbalance_hierarchy()