Description Usage Arguments Details Value Author(s) References See Also Examples

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 *m+1* as *m* tends to infinity (see theorem 3.2 in Prass and Pumi, 2019).

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`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 |

The optional argument *K* is an *m+1* by *m+1* matrix defined by *K = J'QJ*, where *J* is a *m+1* by *m+1* lower triangular matrix with all non-zero entries equal to one and *Q* is a *m+1* by *m+1* given by *Q = I - P* where *P* is the projection matrix into the subspace generated by degree *nu+1* polynomials and *I* is the *m+1* by *m+1* identity matrix. *K* is equivalent to expression (18) in Prass and Pumi (2019).
If this matrix is provided and *m* is an integer, then *nu* are ignored.

A list containing the following elements, calculated considering windows of size *m+1*, for each *m* 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. |

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>.

`Km`

which creates the matrix *K*, `Jn`

which creates the matrix *J*, `Qm`

which creates *Q* and `Pm`

which creates *P*.

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