# cov_kernel: Kernel estimation: bootstrap method In slm: Stationary Linear Models

## Description

This method estimates the spectral density and the autocovariances of the error process via a lag-window (or kernel) estimator (see P.J. Brockwell and R.A. Davis (1991). Time Series: Theory and Methods. Springer Science & Business Media, page 330). The weights are computed according to a kernel K and a bandwidth h (or a lag), to be chosen by the user. The lag can be computed automatically by using a bootstrap technique (as in Wu and Pourahmadi (2009)), via the `Rboot` function.

## Usage

 ```1 2 3``` ```cov_kernel(epsilon, model_selec = -1, model_max = min(50,length(epsilon)/2), kernel_fonc = triangle, block_size = length(epsilon)/2, block_n = 100, plot = FALSE) ```

## Arguments

 `epsilon` numeric vector. An univariate process. `model_selec` integer or `-1`. The order of the method. If `model_selec = -1`, the method chooses the treshold automatically. If `model_selec = k`, then only `k` autocovariance terms are kept and smoothed by the kernel. `model_max` integer. The maximal order. `kernel_fonc` function. Defines the kernel to use in the method. The user can give his own kernel function. `block_size` integer. If `model_selec = -1`, it specifies the size of the bootstrap blocks. `block_size` must be greater than `model_max`. `block_n` integer. If `model_selec = -1`, blocks number to use for the bootstrap. `plot` logical. By default, `plot = FALSE`. If `plot = TRUE`, the risk curve is returned and the ACF of the process.

## Value

The method returns the tapered autocovariance vector with `model_selec` autocovariance terms.

 `model_selec` the number of selected autocovariance terms. `cov_st` the estimated autocovariances.

## References

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.

W.B. Wu, M. Pourahmadi (2009). Banding sample autocovariance matrices of stationary processes. Statistica Sinica, pp. 1755–1768.

## Examples

 ```1 2``` ```x = arima.sim(list(ar=c(0.7)),1000) cov_kernel(x, model_selec = -1, block_n = 10, plot = TRUE) ```

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