| cov_spectralproj {slm} | R Documentation |
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_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, |
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.
See Also
The R package capushe.
Slope heuristic algorithm DDSE.
Dimension jump algorithm Djump.
Examples
x = arima.sim(list(ar=c(0.2), ma=c(0.3,0.05)), n=100)
cov_spectralproj(x, model_selec = -1)