spaceTime              package:fractal              R Documentation

_S_p_a_c_e _t_i_m_e _s_e_p_a_r_a_t_i_o_n _p_l_o_t

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

     This function can be used to generate contours of a space time
     separation plot. This plot type is a visual tool which can help to
     determine the correlation time for a particular delay embedding of
     a given time series.

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

     spaceTime(x, dimension=2, tlag=timeLag(x, method="acfdecor"),
         olag.max=as.integer(min(500,length(x)/20)), probability=0.1)

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

       x: a vector holding a scalar time series

dimension: the desired embedding dimension. Default: '2'.

olag.max: an integer representing the maximum orbital lag ot use in
          forming the results. Default:
          'as.integer(min(500,length(x)/20))'.

probability: a positive numeric scalar on the interval (0,1) which
          gives the probability associated with the first contour. This
          input determines the number of contours to be generated (see
          the output description below). Default: '0.1'.

    tlag: the delay used to create the delay embedding. Default:
          'timeLag(x, method="acfdecor")'.

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

     Each contour, C(p,dt), in a space time separation plot corresponds
     to a particular probability, p, and gives spatial distance between
     pairs of phase space vectors as a function of their temporal
     separation. In particular, any pair of vectors seperated in time
     by dt are separated in the phase space by distance C(p,dt) with
     probability p.

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

     an object of class 'spaceTime'.

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


     _a_s._m_a_t_r_i_x convert the output to a matrix.

     _e_d_a._p_l_o_t plot a summary of the space-time contours including a
          density function estimate of the median contour in addition
          to a suggested range of suitable orbital lags. In the latter
          case, the most populous values of the median contour are
          highlighted by a cross-hatched area that covers a plot of the
          median curve. The suggested range for a suitable orbital lag
          is based on the range of values that first escape this
          cross-hatched region. Optional parameters include:

          _t_y_p_e An integer denoting the type of line to plot ala the
               'par' function. Default: '"l"' (solid line).

          _d_e_n_s_i_t_y The density of the cross-hatched area ala the
               'polygon' function. Default: '10'.

          _a_d_d A logical flag. If 'TRUE', the plot is added using the
               current 'par' settings. Otherwise, the 'par' settings
               are adjusted as needed. Default: 'FALSE'.

          ... Additional parameters sent directly to the 'par'
               function. .in -5


          _p_l_o_t plot the space-time contours for the given 'spaceTime'
               object. Optional arguments include:

               _l_t_y Line type ala the 'par' function. Default: '1'.

               _c_o_l_o_r A vector of integers defining the contour line
                    colors. Default: '1:8'.

               _x_l_a_b A character string denoting the x-axis label.
                    Default: '"Orbital Lag"'.

               _y_l_a_b A character string denoting the y-axis label.
                    Default: '"Spatial Separation"'.

               _m_a_i_n A character string denoting the title label.
                    Default: 'NULL' (no title).

               _c_e_x Character expansion value ala 'par'. Default: '1'.

               _p_c_h An integer representing the plot character ala
                    'par'. Default: '"."'.

               _a_d_d A logical flag. If 'TRUE', the plot is added using
                    the current 'par' settings. Otherwise, the 'par'
                    settings are adjusted as needed. Default: 'FALSE'.

               ... Additional parameters sent directly to the 'par'
                    function. .in -5


               _p_r_i_n_t print a summary of the 'spaceTime' object.

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

     Holger Kantz and Thomas Schreiber, _Nonlinear Time Series
     Analysis_, Cambridge University Press, 1997.

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

     'embedSeries', 'determinism', 'timeLag'.

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

     ## Using the beamchaos data calculate the space 
     ## time separation contours for probabilities 
     ## 1/10, 2/10, ..., 1, for a 3-dimensional 
     ## delay embedding with delay of 10. Plot the 
     ## resulting contours, which will reveal 
     ## periodicity in the data. From the top 
     ## contour in the plot, which corresponds to 
     ## probability 1, we can conclude that any two 
     ## vectors in the chosen delay embedding which 
     ## are separated in time by approximately 90 
     ## time steps are separated by a distance of at 
     ## least 8 in the phase space. 
     z <- spaceTime(beamchaos, dim=3, tlag=10,
         olag.max=500, probability=1/10)

     ## print the results 
     print(z)

     ## plot the results 
     plot(z)

     ## extended data analysis plot 
     eda.plot(z)

