spectrum0 {coda} | R Documentation |
The spectral density at frequency zero is estimated by fitting a glm to
the low-frequency end of the periodogram. spectrum0(x)/length(x)
estimates the variance of mean(x)
.
spectrum0(x, max.freq = 0.5, order = 1, max.length = NULL)
x |
A time series. |
max.freq |
The glm is fitted on the frequency range (0, max.freq] |
order |
Order of the polynomial to fit to the periodogram. |
max.length |
The data x is aggregated if necessary by
taking batch means so that the length of the series is less than
max.length . If this is set to NULL no aggregation occurs. |
The minimum length of the time series. The data x
The raw periodogram is calculated for the series x
and a generalized
linear model with family Gamma
and log link is fitted to
the periodogram.
The linear predictor is a polynomial in terms of the frequency. The
degree of the polynomial is determined by the parameter order
.
spec |
The predicted value of the spectral density at frequency zero. |
Heidelberger and Welch (1991) observed that the usual non-parametric estimator of the spectral density, obtained by smoothing the periodogram, is not appropriate for frequency zero. They proposed an alternative parametric method which consisted of fitting a linear model to the log periodogram of the batched time series. Some technical problems with model fitting in their original proposal can be overcome by using a generalized linear model.
Batching of the data, originally proposed in order to save space, has the side effect of flattening the spectral density and making a polynomial fit more reasonable. Fitting a polynomial of degree zero is equivalent to using the `batched means' method.
The definition of the spectral density used here differs from that used by
spec.pgram
. We consider the frequency range to be between 0 and 0.5,
not between 0 and frequency(x)/2
.
Heidelberger, P and Welch, P.D. A spectral method for confidence interval generation and run length control in simulations. Communications of the ACM, Vol 24, pp233-245, 1981.