Description Usage Arguments Value References See Also Examples

Computes a data-driven histogram estimator of the spectral density of a process and compute its Fourier coefficients,
that is the associated autocovariances. For a dimension *d*, the estimator of the spectral density is an histogram on a regular basis of
size *d*. Then we use a penalized criterion in order to choose the dimension which balance the bias and the variance, as proposed in Comte (2001). The penalty
is of the form *c*d/n*, where *c* is the constant and *n* the sample size. The dimension and the constant of the penalty are
chosen with the slope heuristic method, with the dimension jump algorithm (from package "`capushe`

").

1 2 | ```
cov_spectralproj(epsilon, model_selec = -1,
model_max = min(100,length(epsilon)/2), plot = FALSE)
``` |

`epsilon` |
numeric vector. An univariate process. |

`model_selec` |
integer. The dimension of the method. If |

`model_max` |
integer. The maximal dimension. By default, it is equal to the minimum between 100 and the length of the process divided by 2. |

`plot` |
logical. By default, |

The function returns the estimated autocovariances of the process, that is the Fourier coefficients of the spectral density estimate, and the dimension chosen by the algorithm.

`model_selec` |
the dimension selected. |

`cov_st` |
the estimated autocovariances. |

J.P. Baudry, C. Maugis B. and Michel (2012). Slope heuristics: overview and implementation. *Statistics and Computing*, 22(2), 455–470.

E. Caron, J. Dedecker and B. Michel (2019). Linear regression with stationary errors: the R package slm. *arXiv preprint arXiv:1906.06583*.
https://arxiv.org/abs/1906.06583.

F. Comte (2001). Adaptive estimation of the spectrum of a stationary Gaussian sequence. *Bernoulli*, 7(2), 267-298.

The R package `capushe`

.

Slope heuristic algorithm `DDSE`

.

Dimension jump algorithm `Djump`

.

1 2 |

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