Description
Usage
Arguments
Value
References
See Also
Examples
Packs the parameters defining a specfied stochastic fractal time series
model into a list an returns the result.
 (model, variance.=1.0, delta=0.45,
alpha=0.9, HG=0.95, HB=0.95,
innovations.var=, Cs=,
bterms=10, dterms=10, M=100)

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 socalled Hurst coefficient.
The coefficient Hg is sometimes called
the selfsimilarity parameter for a FGN process
and is usually designated in the literature as simply H.
"dfbm" Discrete Fractional Brownian Motion. i.e., regularlyspaced 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 EulerMaclaurin 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.

an object of class lmModel
containing a list of model parameters.
D. Percival and A. Walden (2000),
Wavelet Methods for Time Series Analysis,
Cambridge University Press, Chapter 7.
J. Beran (1994),
Statistics for LongMemory Processes,
Chapman and Hall, Chapter 2.
D. Percival and A. Walden (1993),
Spectral Analysis for Physical Applications,
Cambridge University Press, 1993, Chapter 9.
lmACF
, lmSDF
, lmSimulate
, lmConvert
, lmConfidence
, FDWhittle
.
 ("ppl", alpha=2.0)
("fdp", delta=0.45, innov=1.3)
("fgn", HG=0.98)
("dfbm", HB=0.35)

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