Description Usage Arguments Value Author(s) References Examples

Calculates the expected value of the detrended variance.

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. |

`G` |
the autocovariance matrix for the original time series. The dimension of |

`K` |
optional: the matrix |

A vector of size *length(m)* containing the expected values of the detrended variance corresponding to the values of *m* provided. This is expression (20) 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 | ```
m = 3
K = Km(m = m, nu = 0)
G = diag(m+1)
EF2dfa(G = G, K = K)
# same as
EF2dfa(m = 3, nu = 0, G = G)
# An AR(1) example
phi = 0.4
n = 500
burn.in = 50
eps = rnorm(n + burn.in)
z.temp = numeric(n + burn.in)
z.temp[1] = eps[1]
for(i in 2:(n + burn.in)){
z.temp[i] = phi*z.temp[i-1] + eps[i]
}
z = z.temp[(burn.in + 1):(n + burn.in)]
F2.dfa = F2dfa(z, m = 3:100, nu = 0, overlap = TRUE)
plot(3:100, F2.dfa, type="o", xlab = "m")
``` |

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