

fracdiff(fracdiff)                           R Documentation

_f_r_a_c_d_i_f_f_: _M_a_x_i_m_u_m _l_i_k_e_l_i_h_o_o_d _p_a_r_a_m_e_t_e_r _e_s_t_i_m_a_t_e_s _f_o_r

_D_e_s_c_r_i_p_t_i_o_n_:

     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 likeli-
     hood.  The likelihood is approximated using the fast
     and accurate method of Haslett and Raftery (1989).

_U_s_a_g_e_:

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

_A_r_g_u_m_e_n_t_s_:

       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)

_V_a_l_u_e_:

     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 esti-
          mates (order : d, ar, ma)

stderror.dpq: standard errors of the parameter estimates
          (order : d, ar, ma)

correlation.dpq: correlation matrix of the parameter esti-
          mates (order : d, ar, ma)

    dtol: interval of uncertainty for d

_M_e_t_h_o_d_:

     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 `lm'DER).  written by
     Chris Fraley (March 1991)

_N_o_t_e_:

     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 prob-
     lems.

_R_e_f_e_r_e_n_c_e_s_:

     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 Deriva-
     tives, 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 Labora-
     tory (August 1980).

_S_e_e _A_l_s_o_:

     `fracdiff.sim'

_E_x_a_m_p_l_e_s_:

     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))

