LongRangeDependence          package:fArma          R Documentation

_S_t_a_t_i_s_t_i_c_s _o_f _t_h_e _T_r_u_e _L_R_D _P_r_o_c_e_s_s

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

     A collection and description of functions  to investigate the true
     statistics of the long range dependence or long memory behavior 
     of an univariate time series process.  

     The Functions are:

     Functions to model the true autocorrelation function and spectrum:

       'fgnTrueacf'         Returns true FGN covariances,
       'fgnTruefft'         returns true FGN fast Fourier transform,
       'fgnStatsSlider'     returns a plot of true FGN Statistics,
       'farimaTrueacf'      returns true FARIMA covariances,
       'farimaTruefft'      returns true FARIMA fast Fourier transform,
       'farimaStatsSlider'  returns a plot of true FARIMA Statistics.

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

        
     fgnTrueacf(n = 100, H = 0.7) 
     fgnTruefft(n = 100, H = 0.7) 
     fgnStatsSlider()

     farimaTrueacf(n = 100, H = 0.7) 
     farimaTruefft(n = 100, H = 0.7)
     farimaStatsSlider()

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

       H: the Hurst exponent, a numeric value between 0.5 and 1, by
          default 0.7. 

       n: number of data points to be simulated, a numeric value,  by
          default 100. 

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

     *Functions to Model True Correlations and Spectrum:* 

     The functions 'fgnTrueacf' and 'farimaTrueacf' return the true
     covariances of an FGN and Gaussian FARIMA(0,d,0) time  series
     process.

     The functions 'fgnTruefft' and 'farimaTruefft' return the true
     fast Fourier transform of an FGN and Gaussian FARIMA(0,d,0)  time
     series process.

     The R functions are implemented from SPlus code written by J.
     Beran [1994].

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

     'fgnTrueacf'
      'farimaTrueacf'
      return the true covariance of an FGN or FARIMA time series
     process. 

     'fgnTruefft'
      'farimaTruefft'
      return the true spectrum of an FGN or FARIMA time series process. 

     fgnStatsSlider()
      farimStatsSlider()
      interactively display the true covariance and the true spectrum
     of an FGN or FARIMA time series process.

_A_u_t_h_o_r(_s):

     J. Beran, ported by Maechler, code as listed in the Appendix of
     his Book, 
      Diethelm Wuertz for the Rmetrics R-port.

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

     Beran J. (1992); _Statistics for Long-Memory Processes_, Chapman
     and Hall, New York, 1994.

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

     ## fgnTrueacf -
        fgnTrueacf(n = 20, H = 0.8)
        
     ## fgnTruefft -
        fgnTruefft(n = 20, H = 0.8)
        
     ## farimaTrueacf -
        farimaTrueacf(n = 20, H = 0.8)
        
     ## farimaTruefft -
        farimaTruefft(n = 20, H = 0.8)

