covFdcca {DCCA} | R Documentation |
Autocovariance function of the detrended cross-covariance
Description
Calculates the autocovariance of the detrended cross-covariance.
Usage
covFdcca(m = 3, nu = 0, h = 0, overlap = TRUE, G1, G2, G12, Cumulants = NULL)
Arguments
m |
an integer or integer valued vector indicating the size of the window for the polinomial fit. |
nu |
a non-negative integer denoting the degree of the polinomial fit applied on the integrated series. |
h |
an integer or integer valued vector indicating the lags for which the autocovariance function is to be calculated. Negative values are not allowed. |
overlap |
logical: if true (the default), overlapping boxes are used for calculations. Otherwise, non-overlapping boxes are applied. |
G1 , G2 |
the autocovariance matrices for the original time series. The dimension of |
G12 |
the cross-covariance matrix for the original time series. The dimension of |
Cumulants |
The matrix of cumulants. If not provided, it is assumed that the cumulants are all zero. |
Value
A matrix of dimension by
with the autocovariance of lag
(rows), for each value of
(columns) provided. This matrix is obtained from expressions (24) for
and (25) for
in Prass and Pumi (2019).
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>.
Examples
## Not run:
ms = seq(3,100,1)
hs = seq(0,50,1)
overlap = TRUE
nu = 0
m_max = (max(ms)+1)*(max(hs)+1) - max(ms)*max(hs)*as.integer(overlap)
theta = c(c(1,(20:1)/10), rep(0, m_max - 20))
Gamma1 = diag(m_max+1)
Gamma2 = matrix(0, ncol = m_max+1, nrow = m_max+1)
Gamma12 = matrix(0, ncol = m_max+1, nrow = m_max+1)
for(t in 1:(m_max+1)){
for(h in 0:(m_max+1-t)){
Gamma2[t,t+h] = sum(theta[1:(length(theta)-h)]*theta[(1+h):length(theta)])
Gamma2[t+h,t] = Gamma2[t,t+h]
Gamma12[t,t+h] = theta[h+1]
}
}
covdcca = covFdcca(m = ms, nu = 0, h = hs,
G1 = Gamma1, G2 = Gamma2, G12 = Gamma12)
## End(Not run)