Description Usage Arguments Value Author(s) References Examples

Calculates the autocovariance of the detrended cross-covariance.

1 |

`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. |

A matrix of dimension *lenght(h)* by *length(m)* with the autocovariance of lag *h* (rows), for each value of *m* (columns) provided. This matrix is obtained from expressions (24) for *h = 0* and (25) for *h > 0* 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>.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
## 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)
``` |

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