RVineStructure¶
- class RVineStructure¶
A class for R-vine structures.
RVineStructure objects encode the tree structure of the vine, i.e. the conditioned/conditioning variables of each edge. It is represented by a triangular array. An exemplary array is
4 4 4 4 3 3 3 2 2 1
which encodes the following pair-copulas:
| tree | edge | pair-copulas | |------|------|----------------| | 0 | 0 | ``(1, 4)`` | | | 1 | ``(2, 4)`` | | | 2 | ``(3, 4)`` | | 1 | 0 | ``(1, 3; 4)`` | | | 1 | ``(2, 3; 4)`` | | 2 | 0 | ``(1, 2; 3, 4)`` |
Denoting by
M[i, j]
the array entry in rowi
and columnj
, the pair-copula index for edgee
in treet
of ad
dimensional vine is(M[d - 1 - e, e], M[t, e]; M[t - 1, e], ..., M[0, e])
. Less formally, 1. Start with the counter-diagonal element of columne
(first conditioned variable). 2. Jump up to the element in rowt
(second conditioned variable). 3. Gather all entries further up in columne
(conditioning set).A valid R-vine array must satisfy several conditions which are checked when
RVineStructure()
is called: 1. It only contains numbers between 1 and d. 2. The diagonal must contain the numbers 1, …, d. 3. The diagonal entry of a column must not be contained in any column further to the right. 4. The entries of a column must be contained in all columns to the left. 5. 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]})
.An R-vine array is said to be in natural order when the anti-diagonal entries are \(1, \dots, d\) (from left to right). The exemplary arrray above is in natural order. Any R-vine array can be characterized by the diagonal entries (called order) and the entries below the diagonal of the corresponding R-vine array in natural order. Since most algorithms work with the structure in natural order, this is how RVineStructure stores the structure internally.
Attributes
dim
The dimension.
order
The variable order.
trunc_lvl
The truncation level.
Methods
Overloaded function.
Randomly sample a regular vine structure.
Converts the structure to a string representation (most useful for printing).
Accesses elements of the structure array.
Write the structure into a JSON file.
Truncates the R-vine structure.