FDSimulate              package:fractal              R Documentation

_S_i_m_u_l_a_t_i_o_n _o_f _a_n _F_D _p_r_o_c_e_s_s _w_i_t_h _t_i_m_e _v_a_r_y_i_n_g _m_o_d_e_l _p_a_r_a_m_e_t_e_r_s

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

     Creates a realization of a time-varying fractionally differenced
     (FD) process with a given vector of FD parameters and
     corresponding vector of innovations variances.

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

     FDSimulate(delta, innovations.var=1, method="ce", seed=0)

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

   delta: a vector containing time-varying FD parameters.

innovations.var: a numeric vector or scalar containing (time-varying)
          FD innovations variances. If a scalar, the value is
          replicated appropriately. Otherwise, the length of this input
          should match the length of the 'delta' vector. Default: '1'.

  method: a character string defining the method to use in forming the
          FD realization. Choices are '"ce"' (circulent emebdding) and
          '"cholesky"'. Default: '"ce"'.

    seed: a positive integer representing the initial seed value to use
          for the random number generator. If 'seed=0', the current
          time is used as a means of generating a (unique) seed value.
          Otherwise, the specified seed value is used. Default: '0'.

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

     a vector containing a (time-varying) FD process realization
     corresponding to the input FD model parameters.

_S_3 _M_E_T_H_O_D_S:


     _p_l_o_t plot the output object. Optional arguments include:

          _s_i_m_u_l_a_t_i_o_n Plot the simulated series. Default: 'TRUE'.

          _d_e_l_t_a Plot the FD parameter as a function of time. Default:
               'TRUE'.

          _i_n_n_o_v_a_t_i_o_n_s._v_a_r Plot the innovations variance as a function
               of time. Default: 'TRUE'. .in -5


          _p_r_i_n_t print the output object.

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

     D. B. Percival and  A. T. Walden, _Wavelet Methods for  Time
     Series Analysis_, Cambridge University Press, 2000.

     D. B. Percival and  W.L.B. Constantine, _Exact Simulations of
     Time-Varying Fractionally Differenced Processes_, submitted to
     Journal of Computational and Graphical Statistics, 2002.

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

     'FDWhittle', 'wavFDPBlock', 'wavFDPTime'.

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

     ## create a time-varying FD parameter, linearly 
     ## varying from white to pink noise, then jump 
     ## to a red noise plateau 
     delta <- c(seq(0, 0.5, by=0.01), rep(1,100))

     ## set the innovations variance to unity 
     innovation <- rep(1, length(delta))

     ## simulate a time-varying FD process 
     z <- FDSimulate(delta=delta, innovation=innovation)
     print(z)
     plot(z)

