polspline (version 1.0.4)

lspec: 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

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). Exac

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

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 fitt

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 pe

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

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.

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

Run this code

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

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