LongMemoryModelling         package:fSeries         R Documentation

_L_o_n_g _M_e_m_o_r_y _B_e_h_a_v_i_o_u_r _o_f _T_i_m_e _S_e_r_i_e_s

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

     A collection and description of functions to investigate the  long
     memory behavior of an univariate time series process. 

     The functions and methods are:

       'fgnSim'  Simulates Fractional Gaussian Noise.

     Sorry, not yet implemented are the functions to fit the Hurst
     exponent.

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

     fgnSim(n = 1000, H = 0.7, method = c("beran", "durbin", "paxson"), 
     mean = 0, std = 1)

_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. 

mean, std: mean and standard deviation of the random innovations. By
          default a zero mean and a unit standard deviation is assumed. 

  method: the method how to generate the time series sequence, one of
          the following character strings: '"beran"',  '"durbin"', or
          '"paxson"'. 

       n: number of data points to be simulated, a numeric value,  by
          default 1000. 

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

     returns a numeric vector of length 'n', the fractional  Gaussian
     noise series.

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

     Paxson V. (1995);  _Fast Approximation of Self-Similar Network
     Traffic_, Berkeley.

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

     ## fgnSim -
        par(mfrow = c(3, 1), cex = 0.75)  
        # Beran's Method:
        plot(fgnSim(n = 200, H = 0.75), type = "l",  
              ylim = c(-3, 3), xlab = "time", ylab = "x(t)", main = "Beran")
        # Durbin's Method:
        plot(fgnSim(n = 200, H = 0.75, method = "durbin"), type = "l",
              ylim = c(-3, 3), xlab = "time", ylab = "x(t)", main = "Durbin")
        # Paxson's Method:
        plot(fgnSim(n = 200, H = 0.75, method = "paxson"), type = "l",
          ylim = c(-3, 3), xlab = "time", ylab = "x(t)", main = "Paxson")

