slm (version 1.2.0)

cov_spectralproj: Data-driven spectral density estimation

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

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<U+2013>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.

See Also

The R package capushe.

Slope heuristic algorithm DDSE.

Dimension jump algorithm Djump.

Examples

# NOT RUN {
x = arima.sim(list(ar=c(0.2), ma=c(0.3,0.05)), n=100)
cov_spectralproj(x, model_selec = -1)
# }