lspec: Lspec: logspline estimation of a spectral distribution

In polspline: Polynomial Spline Routines

Lspec: logspline estimation of a spectral distribution

Description

Fit an lspec model to a time-series or a periodogram.

Usage

lspec(data, period, penalty, minmass, knots, maxknots, atoms, maxatoms,
maxdim , odd = FALSE, updown = 3, silent = TRUE) 

Arguments

data	time series (exactly one of data and period should be specified). If data is specified, lspec first computes the modulus of the fast Fourier transform of the series using the function fft, resulting in a periodogram of length floor(length(data)/2).
period	value of the periodogram for a time series at frequencies \frac{2\pi j}T, for 1\leq j \leq T/2. If period is specified, odd should indicate whether the length of the series T is odd (odd = TRUE) or even (odd = FALSE). Exactly one of data and period should be specified.
penalty	the parameter to be used in the AIC criterion. The method chooses the number of basis functions that minimizes -2 * loglikelihood + penalty * (number of basis functions). Default is to use a penalty parameter of penalty = log(length(period)) as in BIC.
minmass	threshold value for atoms. No atoms having smaller mass than minmass are included in the model. If minmass takes its default value, in 95% of the samples, when data is Gaussian white noise, the model will not contain atoms.
knots	ordered vector of values, which forces the method to start with these knots. If knots is not specified, the program starts with one knot at zero and then employs stepwise addition of knots and atoms.
maxknots	maximum number of knots allowed in the model. Does not need to be specified, since the program has a default for maxdim and the number of dimensions equals the number of knots plus the number of atoms. If maxknots = 1 the fitted spectral density function is constant.
atoms	ordered vector of values, which forces the method to start with discrete components at these frequencies. The values of atoms are rounded to the nearest multiple of \frac{2\pi}T. If atoms is not specified, the program starts with no atoms and then performs stepwise addition of knots and atoms.
maxatoms	maximum number of discrete components allowed in the model. Does not need to be specified, since the program has a default for maxdim and the number of dimensions equals the number of knots plus the number of atoms. If maxatoms = 0 a continuous spectral distribution is fit.
maxdim	maximum number of basis functions allowed in the model (default is \max(15,4\times\mbox{length(period)}^{0.2})).
odd	see period. If period is not specified, odd is not relevant.
updown	the maximal number of times that lspec should go through a cycle of stepwise addition and stepwise deletion until a stable solution is reached.
silent	should printing of information be suppressed?

Value

Object of class lspec. The output is organized to serve as input for plot.lspec (summary plots), summary.lspec (summarizes fitting), clspec (for autocorrelations and autocovariances), dlspec (for spectral density and line-spectrum,) plspec (for the spectral distribution), and rlspec (for random time series with the same spectrum).

call	the command that was executed.
thetap	coefficients of the polynomial part of the spline.
nknots	the number of knots that were retained.
knots	vector of the locations of the knots in the logspline model. Only the knots that were retained are in this vector.
thetak	coefficients of the knot part of the spline. The k-th coefficient is the coefficient of (x-t(k))^3_+.
natoms	the number of atoms that were retained.
atoms	vector of the locations of the atoms in the model. Only the atoms that were retained are in this vector.
mass	The k-th coefficient is the mass at atom[k].
logl	the log-likelihood of the model.
penalty	the penalty that was used.
minmass	the minimum mass for an atom that was allowed.
sample	the sample size that was used, either computed as length(data) or as (2 * length(period)) when odd = FALSE or as (2 * length(period) + 1) when odd = TRUE.
updown	the actual number of times that lspec went through a cycle of stepwise addition and stepwise deletion until a stable solution was reached, or minus the number of times that lspec went through a cycle of stepwise addition and stepwise deletion until it decided to quit.

Author(s)

Charles Kooperberg [e-mail].

References

Charles Kooperberg, Charles J. Stone, and Young K. Truong (1995). Logspline Estimation of a Possibly Mixed Spectral Distribution. Journal of Time Series Analysis, 16, 359-388.

Charles J. Stone, Mark Hansen, Charles Kooperberg, and Young K. Truong. The use of polynomial splines and their tensor products in extended linear modeling (with discussion) (1997). Annals of Statistics, 25, 1371–1470.

See Also

plot.lspec, summary.lspec, clspec, dlspec, plspec, rlspec.

Examples

data(co2)
co2.detrend <- unstrip(lm(co2~c(1:length(co2)))$residuals)
fit <- lspec(co2.detrend)

polspline documentation built on Oct. 27, 2023, 1:07 a.m.