fracdiff: Maximum likelihood parameter estimates for

Usage

fracdiff( x, nar = 0, nma = 0, dtol = <see below>, M = 100)

Arguments

x time series for the ARIMA model
nar number of autoregressive parameters
nma number of moving average parameters
dtol interval of uncertainty for d If dtol is less than zero, the fourth root of machine precision will be used. dtol will be altered if necessary by the program.
M number of terms in the likelihood approximation (see Haslett and Raftery 1989)

Description

Calculates the maximum likelihood estimators of the parameters of a fractionally-differenced ARIMA (p,d,q) model, together (if possible) with their estimated covariance and correlation matrices and standard errors, as well as the value of the maximized likelihood. The likelihood is approximated using the fast and accurate method of Haslett and Raftery (1989).

Value

a list containing the following elements :
log.likelihood logarithm of the maximum likelihood
d optimal fractional-differencing parameter
ar vector of optimal autoregressive parameters
ma vector of optimal moving average parameters
covariance.dpq covarianvce matrix of the parameter estimates (order : d, ar, ma)
stderror.dpq standard errors of the parameter estimates (order : d, ar, ma)
correlation.dpq correlation matrix of the parameter estimates (order : d, ar, ma)
dtol interval of uncertainty for d

Method

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). written by Chris Fraley (March 1991)

Note

Ordinarily nar and nma should not be too large (say < 10) to avoid degeneracy in the model. The function fracdiff.sim is available for generating test problems.

References

J. Haslett and A. E. Raftery, "Space-time Modelling with Long-memory Dependence: Assessing Ireland's Wind Power Resource (with Discussion)", Applied Statistics, 38, 1-50.

R. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall (1973).

J. J. More, B. S. Garbow, and K. E. Hillstrom, Users Guide for MINPACK-1, Technical Report ANL-80-74, Applied Mathematics Division, Argonne National Laboratory (August 1980).

See Also

fracdiff.sim

Examples

ts.test <- fracdiff.sim( 5000, ar = .2, ma = -.4, d = .3)
fracdiff( ts.test$series, nar = length(ts.test$ar), nma = length(ts.test$ma))


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