nse.spec0: Spectral density at zero estimator

View source: R/nse.R

nse.spec0R Documentation

Spectral density at zero estimator


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


  type = c("ar", "glm", "daniell", "modified.daniell", "tukey-hanning", "parzen",
    "triweight", "bartlett-priestley", "triangular", "qs"),
  lag.prewhite = 0,
  welch = FALSE,
  steep = FALSE



A numeric vector.


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".


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.


Use Welch's method (Welsh, 1967) to estimate the spectral density.


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.


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).


The NSE estimator.


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


David Ardia and Keven Bluteau


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.


## Not run: 
n    = 1000
ar   = 0.9
mean = 1
sd   = 1
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 Nov. 10, 2022, 5:52 p.m.