| spec.pgram {stats} | R Documentation |
Estimate Spectral Density of a Time Series by a Smoothed Periodogram
Description
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).
Usage
spec.pgram(x, spans = NULL, kernel, taper = 0.1,
pad = 0, fast = TRUE, demean = FALSE, detrend = TRUE,
plot = TRUE, na.action = na.fail, ...)
Arguments
x |
univariate or multivariate time series. |
spans |
vector of odd integers giving the widths of modified Daniell smoothers to be used to smooth the periodogram. |
kernel |
alternatively, a kernel smoother of class
|
taper |
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. |
pad |
proportion of data to pad. Zeros are added to the end of
the series to increase its length by the proportion |
fast |
logical; if |
demean |
logical. If |
detrend |
logical. If |
plot |
plot the periodogram? |
na.action |
|
... |
graphical arguments passed to |
Details
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.
Value
A list object of class "spec" (see spectrum)
with the following additional components:
kernel |
The |
df |
The distribution of the spectral density estimate can be
approximated by a (scaled) chi square distribution with |
bandwidth |
The equivalent bandwidth of the kernel smoother as defined by Bloomfield (1976, page 201). |
taper |
The value of the |
pad |
The value of the |
detrend |
The value of the |
demean |
The value of the |
The result is returned invisibly if plot is true.
Author(s)
Originally Martyn Plummer; kernel smoothing by Adrian Trapletti, synthesis by B.D. Ripley
References
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
require(graphics)
## Examples from Venables & Ripley
spectrum(ldeaths)
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")