rhoE {DCCA} | R Documentation |
The limit value of the detrended cross-covariance
Description
Calculates the theoretical counterpart of the cross-correlation coefficient. This is expression (11) in Prass and Pumi (2019). For trend-stationary processes under mild assumptions, this is equivalent to the limit of the detrended cross correlation coefficient calculated with window of size as
tends to infinity (see theorem 3.2 in Prass and Pumi, 2019).
Usage
rhoE(m = 3, nu = 0, G1, G2, G12, K = NULL)
Arguments
m |
an integer or integer valued vector indicating the size (or sizes) of the window for the polinomial fit. |
nu |
a non-negative integer denoting the degree of the polinomial fit applied on the integrated series. |
G1 , G2 |
the autocovariance matrices for the original time series. Both are |
G12 |
the cross-covariance matrix for the original time series. The dimension of |
K |
optional: the matrix |
Details
The optional argument is an
by
matrix defined by
, where
is a
by
lower triangular matrix with all non-zero entries equal to one and
is a
by
given by
where
is the projection matrix into the subspace generated by degree
polynomials and
is the
by
identity matrix.
is equivalent to expression (18) in Prass and Pumi (2019).
If this matrix is provided and
is an integer, then
are ignored.
Value
A list containing the following elements, calculated considering windows of size , for each
supplied:
EF2dfa1 , EF2dfa2 |
the expected values of the detrended variances. |
EFdcca |
the expected value of the detrended cross-covariance. |
rhoE |
the vector with the theoretical counterpart of the cross-correlation coefficient. |
Author(s)
Taiane Schaedler Prass
References
Prass, T.S. and Pumi, G. (2019). On the behavior of the DFA and DCCA in trend-stationary processes <arXiv:1910.10589>.
See Also
Km
which creates the matrix ,
Jn
which creates the matrix ,
Qm
which creates and
Pm
which creates .
Examples
m = 3
K = Km(m = m, nu = 0)
G1 = G2 = diag(m+1)
G12 = matrix(0,ncol = m+1, nrow = m+1)
rhoE(G1 = G1, G2 = G2, G12 = G12, K = K)
# same as
rhoE(m = 3, nu = 0, G1 = G1, G2 = G2, G12 = G12)