fracdiff              package: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
     likelihood. 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 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

_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 problems.

_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 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).

_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))

