spec.pgram {stats}R Documentation

Estimate Spectral Density of a Time Series by a Smoothed Periodogram


spec.pgram calculates the periodogram using a fast Fourier transform, and optionally smooths the result with a series of modified Daniell smoothers (moving averages giving half weight to the end values).


spec.pgram(x, spans = NULL, kernel, taper = 0.1,
           pad = 0, fast = TRUE, demean = FALSE, detrend = TRUE,
           plot = TRUE, na.action = na.fail, ...)



univariate or multivariate time series.


vector of odd integers giving the widths of modified Daniell smoothers to be used to smooth the periodogram.


alternatively, a kernel smoother of class "tskernel".


specifies the proportion of data to taper. A split cosine bell taper is applied to this proportion of the data at the beginning and end of the series.


proportion of data to pad. Zeros are added to the end of the series to increase its length by the proportion pad.


logical; if TRUE, pad the series to a highly composite length.


logical. If TRUE, subtract the mean of the series.


logical. If TRUE, remove a linear trend from the series. This will also remove the mean.


plot the periodogram?


NA action function.


graphical arguments passed to plot.spec.


The raw periodogram is not a consistent estimator of the spectral density, but adjacent values are asymptotically independent. Hence a consistent estimator can be derived by smoothing the raw periodogram, assuming that the spectral density is smooth.

The series will be automatically padded with zeros until the series length is a highly composite number in order to help the Fast Fourier Transform. This is controlled by the fast and not the pad argument.

The periodogram at zero is in theory zero as the mean of the series is removed (but this may be affected by tapering): it is replaced by an interpolation of adjacent values during smoothing, and no value is returned for that frequency.


A list object of class "spec" (see spectrum) with the following additional components:


The kernel argument, or the kernel constructed from spans.


The distribution of the spectral density estimate can be approximated by a (scaled) chi square distribution with df degrees of freedom.


The equivalent bandwidth of the kernel smoother as defined by Bloomfield (1976, page 201).


The value of the taper argument.


The value of the pad argument.


The value of the detrend argument.


The value of the demean argument.

The result is returned invisibly if plot is true.


Originally Martyn Plummer; kernel smoothing by Adrian Trapletti, synthesis by B.D. Ripley


Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.

Brockwell, P.J. and Davis, R.A. (1991) Time Series: Theory and Methods. Second edition. Springer.

Venables, W.N. and Ripley, B.D. (2002) Modern Applied Statistics with S. Fourth edition. Springer. (Especially pp. 392–7.)

See Also

spectrum, spec.taper, plot.spec, fft



## Examples from Venables & Ripley
spectrum(ldeaths, spans = c(3,5))
spectrum(ldeaths, spans = c(5,7))
spectrum(mdeaths, spans = c(3,3))
spectrum(fdeaths, spans = c(3,3))

## bivariate example
mfdeaths.spc <- spec.pgram(ts.union(mdeaths, fdeaths), spans = c(3,3))
# plots marginal spectra: now plot coherency and phase
plot(mfdeaths.spc, plot.type = "coherency")
plot(mfdeaths.spc, plot.type = "phase")

## now impose a lack of alignment
mfdeaths.spc <- spec.pgram(ts.intersect(mdeaths, lag(fdeaths, 4)),
   spans = c(3,3), plot = FALSE)
plot(mfdeaths.spc, plot.type = "coherency")
plot(mfdeaths.spc, plot.type = "phase")

stocks.spc <- spectrum(EuStockMarkets, kernel("daniell", c(30,50)),
                       plot = FALSE)
plot(stocks.spc, plot.type = "marginal") # the default type
plot(stocks.spc, plot.type = "coherency")
plot(stocks.spc, plot.type = "phase")

sales.spc <- spectrum(ts.union(BJsales, BJsales.lead),
                      kernel("modified.daniell", c(5,7)))
plot(sales.spc, plot.type = "coherency")
plot(sales.spc, plot.type = "phase")

[Package stats version 3.3.2 Index]