rvinecopulib (version 0.2.6.1.1)

check_rvine_matrix: R-vine matrices

Description

R-vine matrices are compressed representations of the vine structure. It needs to satisfy several properties that can be checked by check_rvine_matrix(), see Details.

Usage

check_rvine_matrix(matrix)

Arguments

matrix

a quadratic matrix, see Details.

Value

Throws an error if matrix is not a valid R-vine matrix, otherwise TRUE is returned invisibly.

Details

The R-vine matrix notation in vinecopulib is different from the one in the VineCopula package. An example matrix is

1 1 1 1
2 2 2 0
3 3 0 0
4 0 0 0

which encodes the following pair-copulas:

tree	edge	pair-copulas
0	0	(4, 1)
	1	(3, 1)
	2	(2, 1)
1	0	(4, 2; 1)
	1	(3, 2; 1)

Denoting by M[i, j] the matrix entry in row i and column j (the pair-copula index for edge e in tree t of a d dimensional vine is (M[d - 1 - t, e], M[t, e]; M[t - 1, e], ..., M[0, e]). Less formally,

1. Start with the counter-diagonal element of column e (first conditioned variable).

2. Jump up to the element in row t (second conditioned variable).

3. Gather all entries further up in column e (conditioning set).

A valid R-vine matrix must satisfy several conditions which are checked when RVineMatrix() is called:

1. The lower right triangle must only contain zeros.

2. The upper left triangle can only contain numbers between 1 and d.

3. The anti-diagonal must contain the numbers 1, ..., d.

4. The anti-diagonal entry of a column must not be contained in any column further to the right.

5. The entries of a column must be contained in all columns to the left.

6. The proximity condition must hold: For all t = 1, ..., d - 2 and e = 0, ..., d - t - 1 there must exist an index j > d, such that (M[t, e], {M[0, e], ..., M[t-1, e]}) equals either (M[d-j-1, j], {M[0, j], ..., M[t-1, j]}) or (M[t-1, j], {M[d-j-1, j], M[0, j], ..., M[t-2, j]}).

Condition 6 already implies conditions 2-5, but is more difficult to check by hand.

Examples

# NOT RUN {
mat <- matrix(c(1, 2, 3, 4, 1, 2, 3, 0, 1, 2, 0, 0, 1, 0, 0, 0), 4, 4)
check_rvine_matrix(mat)

# throws an error
mat[4, 4] <- 5
try(check_rvine_matrix(mat))

# }