lmSDF                package:fractal                R Documentation

_S_D_F _f_o_r _v_a_r_i_o_u_s _s_t_o_c_h_a_s_t_i_c _f_r_a_c_t_a_l _t_i_m_e _s_e_r_i_e_s _m_o_d_e_l_s

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

     Compute a discretized version of a single-sided parametric
     spectral density function (SDF) for various stochastic fractal
     time series models.

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

     lmSDF(x, sampling.interval=1, n.freq=NULL,
         n.sample=NULL, with.Nyquist=NULL)

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

       x: an object of class '"lmModel"'. Use the 'lmModel' function to
          create this input.

  n.freq: the number of frequencies at which the SDF is computed (this
          argument should not be supplied if 'n.sample' is supplied).
          If 'n.sample' is non-NULL supplied but 'n.freq' is NULL, the
          actual grid of frequencies is determined by the argument
          with.Nyquist. Default: if neither 'n.sample' nor 'n.freq' is
          specified, 'n.freq' defaults to 32.

n.sample: length of a time series. If non-NULL, the spectral resolution
          is set to '1/(n.sample * sampling.interval)'. Default: 'NULL'
          ('n.freq' is used to set the specral resolution instead).

sampling.interval: the sampling interval for the process. The SDF is
          computed for frequencies on the interval [0, Nyquist] where
          Nyquist is '1/(2*sampling.interval)'. The value of
          'sampling.interval' must be a positive number. Default: '1'.

with.Nyquist: a logical flag. If 'TRUE', the grid of frequencies over
          which the SDF is evaluated ranges from
          1/2*n.freq*sampling.interval up to the Nyquist frequency;
          otherwise, the range is from 1/(2*n.freq +
          1)*sampling.interval to just below the Nyquist frequency. The
          intent of this argument is to mimic the grid of Fourier
          frequencies for time series with an even or odd sample size
          by setting with.Nyquist to, respectively, 'TRUE' or 'FALSE'.
          This argument is only really intended to be used if
          'n.sample' is not supplied, but 'n.freq' is. Default: 'TRUE'.

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

     The SDF is computed as described in Section 7.6 of Percival and
     Walden (2000), after a possible change of variable to take into
     account the sampling interval (the discussion in the reference
     assumes a unit sampling interval).

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

     an object of class 'signalSeries' containing the SDF.

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

     D. Percival and A. Walden (2000), _Wavelet Methods for Time Series
     Analysis_, Cambridge University Press, Chapter 7.

     J. Beran (1994), _Statistics for Long-Memory Processes_, Chapman
     and Hall, Chapter 2.

     D. Percival and A. Walden (1993), _Spectral Analysis for Physical
     Applications_, Cambridge University Press, 1993, Chapter 9.

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

     'lmModel', 'lmACF', 'lmSimulate'.

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

     old.plt <- par("plt")
     models <- c("ppl","fdp","fgn","dfbm")
     for (i in seq(along=models)){
         splitplot(2,2,i)
         plot(lmSDF(lmModel(models[i])),
         reference.grid=FALSE, log.axes="xy")
     }
     par(plt=old.plt)

