# nse.spec0: Spectral density at zero estimator In nse: Numerical Standard Errors Computation in R

## Description

Function which calculates the numerical standard error with the spectrum at zero estimator.

## Usage

 ```1 2 3 4 5 6 7 8``` ```nse.spec0( x, type = c("ar", "glm", "daniell", "modified.daniell", "tukey-hanning", "parzen", "triweight", "bartlett-priestley", "triangular", "qs"), lag.prewhite = 0, welch = FALSE, steep = FALSE ) ```

## Arguments

 `x` A numeric vector. `type` Method to use in estimating the spectral density function, among `"ar"`, `"glm"`, `"daniell"`, `"modified.daniell"`, `"tukey-hanning"`, `"parzen"`, `"triweight"`, `"bartlett-priestley"`, `"triangular"`, and `"qs"`. See *Details*. Default is `type = "ar"`. `lag.prewhite` Prewhite the series before analysis (integer or `NULL`). When `lag.prewhite = NULL` this performs automatic lag selection. Default is `lag.prewhite = 0` that is no prewhitening. `welch` Use Welch's method (Welsh, 1967) to estimate the spectral density. `steep` Use steep or sharp version of the kernel (Phillips et al., 2006) (only available for type: `"qs"`,`"triangular"`, and `"parzen"`). `lag.prewhite` must be set to 0 to use steep version.

## Details

Welsh's method use 50% overlap and 8 sub-samples. The method `"ar"` estimates the spectral density using an autoregressive model, `"glm"` using a generalized linear model Heidelberger & Welch (1981), `"daniell"` uses daniell window from the R kernel function, `"modified.daniell"` uses daniell window the R kernel function, `"tukey-hanning"` uses the tukey-hanning window, `"parzen"` uses the parzen window, `"triweight"` uses the triweight window, `"bartlett-priestley"` uses the Bartlett-Priestley window, `"triangular"` uses the triangular window, and `"qs"` uses the quadratic-spectral window,

This kernel based variance estimator apply weights to smooth out the spectral density using a kernel and takes the spectral density at frequency zero which is equivalent to the variance of the serie. Bandwidth for the kernel is automatically selected using cross-validatory methods (Hurvich, 1985).

## Value

The NSE estimator.

## Note

`nse.spec0` relies on the packages `coda`; see the documentation of this package for more details.

## Author(s)

David Ardia and Keven Bluteau

## References

Heidelberger, P., Welch, Peter D. (1981). A spectral method for confidence interval generation and run length control in simulations. Communications of the ACM 24(4), 233-245.

Phillips, P. C., Sun, Y., & Jin, S. (2006). Spectral density estimation and robust hypothesis testing using steep origin kernels without truncation. International Economic Review, 47(3), 837-894.

Welch, P. D. (1967), The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Transactions on Audio and Electroacoustics, AU-15(2): 70-73,

Hurvich, C. M. (1985). Data-driven choice of a spectrum estimate: extending the applicability of cross-validation methods. Journal of the American Statistical Association, 80(392), 933-940.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## Not run: n = 1000 ar = 0.9 mean = 1 sd = 1 set.seed(1234) x = c(arima.sim(n = n, list(ar = ar), sd = sd) + mean) nse.spec0(x = x, type = "parzen", lag.prewhite = 0, welch = TRUE, steep = TRUE) ## End(Not run) ```

nse documentation built on April 26, 2021, 1:06 a.m.