FNS                 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 Strands (FNS) to estimate the
     minimal embedding dimension of a multivariate data set.

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

     FNS(x, dimension=5, tlag=NULL, atol=1,
         image.tol=1, olag=1)

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

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

    atol: fNS statitstic threshold. Default: '1'.

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

image.tol: an integer defining the so-called iterate tolerance. Nearest
          neighbor pairs (i,J(i)) are separated in time by a point
          index span dindex = |i-J(i)|, where J(i) represents the index
          of the nearest neighbor to point i. If a point near i, say k
          points away also has a nearest neighbor such that |k - J(k)|
          = dindex +/- M, where M is the iterate tolerance, then the
          pair (k, J(k)) is added to the current strand. Typically, M=0
          or M=1. If M=0, then the difference in index must be exactly
          the same for each pair included in the strand. If M=1, the
          index difference is allowed to be 1 point off from the
          reference pair.  Default: '1'.

    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: '1'.

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

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

     The statistic used for determining a false nearest strand (FNS) is
     based on a Euclidean tolerance supplied by the user ('atol'). Let
     S(d) be the mean Euclidean distance in the projected (d+1)th
     coordinate between strand pairs found to be nearest neighbors in
     embedding dimension $d$. If S(d) / A > atol, where A is the
     estimated attractor size, then the strand is considered to be a
     false strand. A is typically calculated to be the sample standard
     deviation of the original time series. The S(d) statistic is a
     measure of the average additional Euclidean distance we gain by
     embedding the strand in the next dimension, and is used to assess
     when this extra distance has grown too large, indicating a false
     strand.

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

     an single-dimensional matrix containing the FNS percentage as a
     function of embedding dimension.

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

     M. B. Kennel and Henry D.I. Abarbanel (2002), False neighbors and
     false strands: A reliable minimum embedding dimension algorithm,
     _Physical Review E_, *66*, 026209, 1-19.

     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:

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

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

     ## perform False Nearest Strands 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 <- FNS(beamchaos, dim=10, tlag=10, olag=15)

     ## print the results 
     print(x)

