lmModel: Constructor function for objects of class "lmModel"

In fractal: A Fractal Time Series Modeling and Analysis Package

Description

Packs the parameters defining a specfied stochastic fractal time series model into a list an returns the result.

Usage

lmModel(model, variance.=1.0, delta=0.45,
    alpha=-0.9, HG=0.95, HB=0.95,
    innovations.var=NULL, Cs=NULL,
    bterms=10, dterms=10, M=100)

Arguments

model	a character string defining the model type. Choices are "ppl" Pure power law (PPL) process. A process {X(t)} is a PPL process if its SDF is given by S(X,f) = Cs * |f|\eqn{\mbox{\textasciicircum}}{^}alpha where Cs > 0. The innovations variance for this process is given by Cs * exp(-alpha*(log(2)+1)) (this is the variance of the best linear predictor of the process given its infinite past). "fdp" Fractionally differenced (FD) process. A process {X(t)} is a FD process if its SDF is given by S(X,f) = sigma^2 / (2 * sin(pi*f) )^(2 * delta) for |f| <= 1/2 where sigma^2 is the innovations variance, and delta is the FD parameter. Thus, an FD model is completely defined by the innovations variance and FD parameter. "fgn" Fractional Gaussian noise (FGN) process. An FGN process {X(t)} is a stationary Gaussian process if its ACVF is given by s(X,k) = var{X}/2 *(|k + 1|^(2*Hg) - 2*|k|^(2*Hg) + |k + 1|^(2*Hg)) where var{X} > 0 is the variance of the process, while Hg is the so-called Hurst coefficient. The coefficient Hg is sometimes called the self-similarity parameter for a FGN process and is usually designated in the literature as simply H. "dfbm" Discrete Fractional Brownian Motion. i.e., regularly-spaced samples from a FBM process that is defined over the entire real axis.
Cs	pure power law constant. If supplied, this argument is used to compute variance and innovations.var. If not supplied and innovations.var is supplied, then Cs and variance are determined from the innovations.var. Default: NULL.
HB	the Hurst coefficient for a DFBM process. Default: 0.95.
HG	the Hurst coefficient for an FGN process. Default: 0.95.
M	sets the number of terms used in the Euler-Maclaurin summation for calculating the SDF of an FGN process and DFBM process. The default value should be adequate for all values of the Hurst coefficient. Default: 100.
alpha	power law exponent for a PPL model. Default: -0.9.
bterms	an integer used to control the number of primary terms cumulatively summed in computing an ACVS for a PPL process. Default: 10.
delta	the FD parameter. Default: 0.45.
dterms	an integer used to control the number of secondary terms cumulatively summed in computing an ACVS for a PPL process. Default: 10.
innovations.var	innovations variance for an FD or PPL model. If supplied, this argument is used to compute variance and, for a PPL model, Cs. If not supplied and Cs is supplied for a PPL model, then Cs determines innovations.var. If not supplied and Cs is also not supplied for a PPL model or if not supplied for an FD model, then variance determines innovations.var. Default: NULL.
variance.	the process variance with a default of unity. If cs or innovations.var is specified, this parameter is set in agreement with those. If the process is nonstationary but has stationary differences, i.e., incrementally stationary, then the process variance is taken to be the variance of the stationary process that is formed by appropriately differencing the nonstationary process.

Value

an object of class lmModel containing a list of model parameters.

References

D. Percival and A. Walden (2000), Wavelet Methods for Time Series Analysis, Cambridge University Press, Chapter 7.

J. Beran (1994), Statistics for Long-Memory Processes, Chapman and Hall, Chapter 2.

D. Percival and A. Walden (1993), Spectral Analysis for Physical Applications, Cambridge University Press, 1993, Chapter 9.

See Also

lmACF, lmSDF, lmSimulate, lmConvert, lmConfidence, FDWhittle.

Examples

lmModel("ppl", alpha=-2.0)
lmModel("fdp", delta=0.45, innov=1.3)
lmModel("fgn", HG=0.98)
lmModel("dfbm", HB=0.35)

fractal documentation built on May 1, 2019, 8:04 p.m.