arima.fracdiff(x, model, d.tol = <<see below>>, h = <<see below>>, M = 100, d.range = c(0,.5))
d
,
ar
,
ma
, where
d
is the initial fractional differencing parameter (0 <
d
< .5).
Default : NA
ar
is the vector of initial values for the autoregressive parameters.
Its length is the number of
ar
parameters that will be returned.
An initial value of 0 is assumed for all components that are not
assigned values.
Default: NULL
ma
is the vector of initial values for the moving average parameters.
Its length is the number of
ma
parameters that will be returned.
An initial value of 0 is assumed for all components that are not
assigned values.
Default: NULL
d
.
This should be a small positive quantity.
If
d.tol
is initially nonpositive, too large in magnitude, or too
small in magnitude for the achievable accuracy, it will be automatically
altered by the program.
Default: the fourth root of machine (double) precision.
d
in estimating
var.coef
.
This should be a small positive quantity
such that a perturbation of
d
by
h
produces a
small but nonnegligeable perturbation in the likelihood.
If
h
is initially not assigned, nonpositive,
or unreasonably large or small in magnitude,
it will be automatically altered by the program.
d
is to be optimized. Default:
c(0,.5)
.
d
,
ar
, and
ma
d
,
ar
,
ma
)
d
ultimately used by the method.
var.coef
.
var.coef
with a different
finite-difference interval.
Ordinarily the number of
ar
and
ma
parameters should not be too large
(say < 10) to avoid degeneracy in the model.
The optimization is carried out in two levels : an outer univariate unimodal
optimization in
d
over the interval [0,.5]
(uses Brent's fmin algorithm), and
an inner nonlinear least-squares optimization in the
ar
and
ma
parameters
to minimize white noise variance (uses the MINPACK subroutine LMDER).
Haslett, J. and Raftery, A. E. (1989).
Space-time modeling with long-memory dependence:
assessing Ireland's wind power resource (with discussion).
Applied Statistics
38, 1-50.
Brent, R. (1973).
Algorithms for Minimization without Derivatives.
Englewood Cliffs, NJ : Prentice-Hall.
More, J. J., Garbow, B. S., and Hillstrom, K. E. (1980).
Users Guide for MINPACK-1.
Technical Report ANL-80-74,
Applied Mathematics Division, Argonne National Laboratory.
The chapter "Analyzing Time Series" of the S-PLUS Guide to Statistical and Mathematical Analysis.
# generate a fractionally-differenced ARIMA(1,d,1) model given initial values ts.sim <- arima.fracdiff.sim(model = list(d=.3, ar=.2, ma=.4), n = 3000) # estimate the parameters in an ARIMA(1,d,1) model for the simulated series arima.fracdiff(ts.sim, model = list(ar = NA, ma = NA))