FNN                 package:fractal                 R Documentation

_E_s_t_i_m_a_t_i_o_n _o_f _t_h_e _p_r_o_p_e_r _e_m_b_e_d_d_i_n_g _d_i_m_e_n_s_i_o_n _f_o_r _a _s_i_n_g_l_e-_v_a_r_i_a_b_l_e _t_i_m_e _s_e_r_i_e_s

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

     Invokes the method of False Nearest Neighbors (FNN) to estimate
     the minimal embedding dimension of a multivariate data set.

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

     FNN(x, dimension=5, tlag=NULL, rtol=10, atol=2, olag=1)

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

       x: a vector containing a uniformly-sampled real-valued time
          series.

    atol: neighbor tolerance based on attractor size. If the Euclidean
          distance between two neighbor candidates is 'Atol' times
          larger the estimated "size" of the attractor, then those
          neighbors are declared as false neighbors. Default: '2'.

dimension: the maximal embedding dimension. Default: '5'.

    olag: orbital lag. The number of points along the trajectory
          (orbit) of the current point that must be exceeded in order
          for another point in the phase space to be considered a
          neighbor candidate. This argument is used to help attenuate
          temporal correlation in the the embedding which can lead to
          spuriously low minimal embedding dimension estimates. The
          orbital lag must be positive or zero. Default: '0'.

    rtol: false neighbor Euclidean distance tolerance. If the ratio of
          the Euclidean distances between neighbor candidates in
          successive embedding dimensions exceeds 'Rtol', then those
          neighbors are declared as false neighbors. For example, if
          'Rtol=5' neighbor candidates that are separated five times
          more so than in the previous embedding dimension are declared
          false neighbors. Default: '10'.

    tlag: the time delay between coordinates. Default: the
          decorrelation time of the autocorrelation function.

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

     an object of class 'FNN'.

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


     _p_l_o_t plots a summary of the results. Available options are:

          _x_l_a_b a character string defining the x-axis label. Default:
               '"Embedding Dimension"'.

          _y_l_a_b a character string defining the y-axis label. Default:
               '"FNN percentage"'.

          '...' Additional plot arguments (set internally by the 'par'
               function). .in -5


          _p_r_i_n_t prints a summary of the results. Available options are:

               ... Additional print arguments used by the standard
                    'print' function. .in -5


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

     M. B. Kennel, R. Brown, and H. D. I. Abarbanel (1992), Determining
     embedding dimension for phase-space reconstruction using a
     geometrical construction, _Physical Review A_, *45*(6), 3403-3411.

     Fredkin, D. R., and Rice, J. A. (1995), Method of false nearest
     neighbors: A cautionary note, _Physical Review E_, *51*(4),
     2950-2954.

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

     'FNS', 'embedSeries', 'infoDim', 'corrDim', 'timeLag',
     'determinism'.

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

     ## perform False Nearest Neighbors tests on 
     ## chaotic beam data for embedding dimensions 1 
     ## through 10, using a time delay embedding 
     ## with a time lag of 10 and an orbital lag of 
     ## 15 
     x <- FNN(beamchaos, tlag=10, olag=15 )

     ## print the results 
     print(x)

     ## plot the results 
     plot(x)

