lmACF                package:fractal                R Documentation

_A_C_F, _P_A_C_F, _a_n_d _A_C_V_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:

     Computes the autocovariance, autocorrelation or partial
     autocorrelation sequences for various stochastic fractal time
     series models.

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

     lmACF(x, lag.max=32, type="correlation")

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

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

 lag.max: the maximum number of lags at which to compute the
          autocovariance, the autocorrelation or the partial
          autocorrelation. Default: '32'.

    type: a character string defining the output type based on the
          following options:

          "_c_o_v_a_r_i_a_n_c_e" autocovariance sequence

          "_c_o_r_r_e_l_a_t_i_o_n" autocorrelation sequence

          "_p_a_r_t_i_a_l" partial autocorrelation sequence .in -5

               Default: '"correlation"'.

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

     The autocovariance sequence is computed using Equation (2.10) of
     Beran (1994). The autocorrelation sequence is computed by dividing
     the autocovariance sequence by the variance of the process (i.e.,
     the value of the autocovariance sequence at lag zero). The partial
     autocorrelation sequence is computed using the Levinson-Durbin
     recursions.

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

     an object of class 'signalSeries' containing the result.

_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', 'lmSDF', 'lmSimulate', 'ACVStoPACS'.

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

     models <- c("ppl","fdp","fgn")
     lag <- 100
     z <- lapply(models, function(x, models, lag)
         { lmACF(lmModel(x), lag=lag)@data},
         models=models, lag=lag)
     names(z) <- paste(upperCase(models), "ACF")
     stackPlot(seq(0,lag), z, xlab="lag")
     title("Stochastic Fractal Model ACFs")

