FDWhittle              package:fractal              R Documentation

_E_s_t_i_m_a_t_e _t_h_e _H_u_r_s_t _c_o_e_f_f_i_c_i_e_n_t _b_y _W_h_i_t_t_l_e'_s _m_e_t_h_o_d

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

     Using an estimate of the spectral density function for an input
     time series, Whittle's method fits the parameters of a specified
     SDF model to the data by optimizing an appropriate functional. In
     this case, the SDF for a fractionally differenced (FD) process
     model is used and an estimate of (delta), the FD parameter, is
     returned.

_U_s_a_g_e:

     FDWhittle(x, method="continuous", dc=FALSE, freq.max=0.5,
         delta.min=-1,delta.max=2.5, sdf.method="direct", ...)

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

       x: a vector containing a uniformly-sampled real-valued time
          series.

     ...: optional SDF estimation arguments passed directly to the
          'SDF' function. See help documentation for the 'SDF' function
          for more information.

      dc: a logical value. If 'FALSE', the DC component of the SDF
          (corresponding to the sample mean of the series) is not used
          in optimizing the Whittle functional. Default: 'FALSE'.

delta.max: the maximum value for the FD parameter to use in the
          constrained optimization problem. Default: '2.5'.

delta.min: the minimum value for the FD parameter to use in the
          constrained optimization problem. Default: '-1'.

freq.max: the largerst normalized frequency of the SDFs use in the
          analysis. Default: '0.25'.

  method: a character string indicating the method to be used in
          estimating the Hurst coefficient (H). Choices are:

          '"_c_o_n_t_i_n_u_o_u_s"' Whittle's method using a continuous model
               approach to form the optimization functional. This
               functional is subsequently implemented via a discrete
               form of the SDF for an FD process.

          '"_d_i_s_c_r_e_t_e"' Whittle's method using (directly) a discrete
               form of the SDF for an FD process. .in -5

               Default: '"continuous"'.

sdf.method: a character string denoting the method to use in estimating
          the SDF. Choices are '"direct"', '"lag window"', '"wosa"'
          (Welch's Overlapped Segment Averaging), '"multitaper"'. See
          help documentation for the 'SDF' function for more
          information. Default: '"direct"'.

_V_a_l_u_e:

     estimate of the FD parameter of the time series.

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

     M. S. Taqqu and V. Teverovsky, On Estimating the Intensity of
     Long- Range Dependence in Finite and Infinite Variance Time Series
     (1998), in _A practical Guide to Heavy Tails: Statistical
     Techniques and Applications_, pp. 177-217, Birkhauser, Boston.

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

     'hurstSpec', 'FDSimulate'.

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

     set.seed(100)
     walk <- cumsum(rnorm(1024))
     FDWhittle(walk, method="discrete", sdf.method="multitaper")
     FDWhittle(walk, method="continuous", sdf.method="multitaper")

