Description Usage Arguments Details Value Theory Note References See Also

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)`

.

1 |

`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 |

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`

.

A list with the following values

`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`

.

The model fitting may fail on chains with very high autocorrelation.

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.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.