DCCA (version 0.1.1)

EFdcca: Expected value of the detrended cross-covariance

Description

Calculates the expected value of the detrended cross-covariance given a cross-covariance matrix.

Usage

EFdcca(m = 3, nu = 0, G, K = NULL)

Arguments

m

an integer or integer valued vector indicating the size of the window for the polinomial fit. \(min(m)\) must be greater or equal than \(nu\) or else it will result in an error.

nu

a non-negative integer denoting the degree of the polinomial fit applied on the integrated series.

G

the cross-covariance matrix for the original time series. The dimension of \(G\) must be \((max(m)+1)\) by \((max(m)+1)\).

K

optional: the matrix \(K\). If this matrix and \(m\) are provided, then \(nu\) is ignored.

Value

a size \(length(m)\) vector containing the expected values of the detrended cross-covariance corresponding to the values of \(m\) provided. This is expression (23) in Prass and Pumi (2019).

References

Prass, T.S. and Pumi, G. (2019). On the behavior of the DFA and DCCA in trend-stationary processes <arXiv:1910.10589>.

Examples

# NOT RUN {
m = 3
K = Km(m = m, nu = 0)
G = diag(m+1)
EFdcca(G = G, K = K)
# same as
EFdcca(m = 3, nu = 0, G = G)


# }