Km {DCCA} | R Documentation |
This is an auxiliary function which computes expression (18) in Prass and Pumi (2019). It creates an m+1
by m+1
matrix defined by K = J'QJ
where J
is a m+1
by m+1
lower triangular matrix with all non-zero entries equal to one and Q
is a m+1
by m+1
given by Q = I - P
where P
is the projection matrix into the subspace generated by degree nu+1
polynomials and I
is the m+1
by m+1
identity matrix.
Km(m = 3, nu = 0, J = NULL, Q = NULL)
m |
a positive integer greater or equal than |
nu |
a non-negative integer denoting the degree of the polinomial fit applied on the integrated series. |
J , Q |
optional: the matrices such that |
an m+1
by m+1
matrix corresponding to expression (18) in Prass and Pumi (2019).
Taiane Schaedler Prass
Prass, T.S. and Pumi, G. (2019). On the behavior of the DFA and DCCA in trend-stationary processes <arXiv:1910.10589>.
Jn
which creates the matrix J
, Qm
which creates Q
and Pm
which creates P
.
K = Km(m = 3, nu = 0)
K
# same as
m = 3
J = Jn(n = m+1)
Q = Qm(m = m, nu = 0)
K = Km(J = J, Q = Q)
K