# cov_spectralproj: Data-driven spectral density estimation In slm: Stationary Linear Models

## Description

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`").

## Usage

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

## Arguments

 `epsilon` numeric vector. An univariate process. `model_selec` integer. The dimension of the method. If `model_selec = -1`, the method works automatically and take a dimension between 1 and `model_max`. `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, `plot = FALSE`. If `plot = TRUE`, plot the spectral density estimator of the process.

## Value

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.

## References

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`.

## Examples

 ```1 2``` ```x = arima.sim(list(ar=c(0.2), ma=c(0.3,0.05)), n=100) cov_spectralproj(x, model_selec = -1) ```

slm documentation built on Aug. 31, 2020, 5:11 p.m.