hurstACVF              package:fractal              R Documentation

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

     Estimates long memory parameters beta (ACVF decay exponent), alpha
     (Equivalent PPL model spectral density exponent), and H
     (Equivalent Hurst parameter) by linear regression of scaled asinh
     of ACVF versus log(lag) over intermediate lag values.

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

     hurstACVF(x, Ascale=1000, lag.min=1, lag.max=64)

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

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

  Ascale: scale factor for use in the scaled asinh plot. Default:
          '1000'.

 lag.max: maximum lag for use in linear regression. Default: '64'.

 lag.min: minimum lag for use in linear regression. Default: '1'.

_D_e_t_a_i_l_s:

     Evaluates autocovariance function (ACVF) of input time series by
     call to S-Plus function 'acf'. Constructs sequence asinh(Ascale *
     ACVF) / asinh(Ascale) and does linear regression (via S-Plus
     function "lsfit") of this sequence versus log(lag) from 'lag.min'
     to 'lag.max'. Draws a plot of the sequence and the fit line.
     Recommended usage: look at resulting plot. Is the intermediate
     range approximately linear? If plot is too flat, decrease Ascale.
     If it decreases to zero too quickly, increase Ascale. Values of
     Ascale from 10 to 10^6 have been found useful. If 'lag.min' and
     'lag.max' do not bound the range where the sequence is
     approximately linear then change them and rerun the function to
     produce a better fit.

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

     a list with three components:

    beta: decay exponent of autocovariance function

   alpha: spectral density exponent of equivalent PPL model

       H: Hurst exponent for equivalent ACVF decay rate

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

     A. G. Gibbs and D. B. Percival, Forthcoming paper on the
     autocovariance of the PPL (pure power law) model. A section of the
     paper discusses the usefulness of scaled asinh plots.

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

     'hurstBlock'.

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

     hurstACVF(nile, Ascale=1000000, lag.min=3, lag.max=68)

