timeLag               package:fractal               R Documentation

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

     Given the time series X(t), the embedding dimension E, and the
     time lag tau, the embedding coordinates are defined as X(t), X(t +
     tau), ... , X(t + (E - 1)*tau). This function can be used to
     estimate the time lag tau using a variety of statistical methods.

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

     timeLag(x, method="acfzero", plot.data=FALSE)

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

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

  method: character string denoting the method to use in estimating the
          time delay. Supported methods are:

          '"_a_c_f_z_e_r_o"' First zero crossing of the autocorrelation
               function.

          '"_a_c_f_d_e_c_o_r"' First 1/e of the autocorrelation function.

          '"_a_c_f_n_a_d_i_r"' First nadir of the autocorrelation function.

          '"_m_u_t_u_a_l"' First nadir of the average mutual information
               function. .in -5

               Default: '"acfzero"'.

plot.data: a logical value. If 'TRUE', a plot of the time lag selection
          process is displayed. Default: 'FALSE'.

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

     Currently, there exists no single method which yields an optimal
     time lag estimation although there are some basic criteria that
     are used: if the lag is chosen too small, the coordinates will be
     too highly correlated and the embedding will cluster tightly
     around the diagonal in the phase space. If the lag is chosen too
     large, the resulting coordinates may be almost uncorrelated and
     the resulting embedding may become unduly complicated, even if the
     underlying attractor is not. The goal is to find a lag which falls
     in-between these scenarios.

     In addition the autocorrelation-based methods this function
     supports an estimation method based on the time-delayed mutual
     infomation (TDMI), which can be thought of as a nonlinear
     generalization of the autocorrelation function. For a random
     process X(t) the TDMI, I(tau), is a measure of the information
     about X(t+tau) contained in X(t). The first nadir of I(tau) gives
     the delay, tau0, such that X(t+tau0) adds maximal information to
     that already known from X(t). This tau0 is returned as an estimate
     of the proper time lag for a delay embedding of the given time
     series.

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

     an integer representing the the estimated time lag.

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

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

     J.B. Bassingthwaighte and L.S. Liebovitch and B.J. West (1994),
     _Fractal Physiology_, Oxford University Press, New York.

     A.M. Fraser and H.L. Swinney (1986), Independent coordinates for
     strange attractors from mutual information, _Physical Review A_,
     *33*, 1134-40.

     M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson (1991), State
     Space Reconstruction in the Presence of Noise, _Physica D_, *51*,
     52- 98.

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

     'embedSeries', 'infoDim', 'corrDim', 'lyapunov', 'findNeighbors',
     'KDE', 'determinism'.

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

     ## estimate the proper time lag for an embedding 
     ## of the beamchaos data using the first zero 
     ## crossing of the ACF 
     as.numeric(timeLag(beamchaos, method="acfzero", plot=TRUE))

