nse (version 1.21)

nse.spec0: Spectral density at zero estimator

Description

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

Usage

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
)

Value

The NSE estimator.

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.

Author

David Ardia and Keven Bluteau

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).

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

if (FALSE) {
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)
}