

amif(tseries)                                R Documentation

_A_u_t_o _M_u_t_u_a_l _I_n_f_o_r_m_a_t_i_o_n _F_u_n_c_t_i_o_n

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

     Computes and plots the sample (normalized) auto mutual
     information function of `x' up to lag `lag.max'. If
     `plot' is `TRUE', then the AMIF is plotted. Also the
     confidence bound for the null of surrogate data is com-
     puted by Monte-Carlo simulation percentiles and plot-
     ted. If any temporal dependence is under question, then
     the null is an i.i.d. series and scrambled surrogates
     can be used (the default). In the case of testing non-
     linearity against linearity, setting the switch `fft'
     is appropriate. It generates surrogates with the same
     spectrum as `x'. If the switch `amplitude' is set in
     addition, then surrogates `xs' with the following prop-
     erties are used: First, `xs' has the same histogram as
     `x'. Second, `G(xs)' has the same Fourier spectra as
     `G(x)', where `G(.)' is the transformation from the
     histogram of `x' to a Gaussian distribution.

     The simulations are computed with the actual values of
     `maxbit' and `confidence'.

     Missing values are not allowed.

_U_s_a_g_e_:

     amif (x, lag.max = NULL, maxbit = 20, confidence = 0.2, ci = 0.95, nsurr = 20,
           fft = FALSE, amplitude = FALSE, normalized = TRUE, trace = FALSE,
           plot = TRUE, ...)
     plot (obj, ci.col = "blue", ...)

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

       x: a numeric vector or time series.

 lag.max: a scalar lag parameter.

  maxbit: the maximum resolution in bit to which the preci-
          sion of the data will be limited; also limits the
          maximum partition depth. It cannot exceed an over-
          all maximum of 25 bit.

confidence: the confidence level for the chi-square-test
          which tests the point distribution in substruc-
          tures of the probability area upon uniformity. A
          substructure is assumed if the deviation from a
          uniform point distribution occurs with a probabil-
          ity less than the significance niveau. Possible
          settings are: 0.01, 0.02, 0.05, 0.1, 0.2, ...,
          0.9, 0.95, 0.98, 0.99.

      ci: coverage probability for confidence bound. Plot-
          ting of the confidence bound is suppressed if `ci'
          is zero or negative.

   nsurr: the number of surrogate samples to compute the
          confidence bound. To obtain "good" confidence
          bounds, set `nsurr' to at least a value of `500'.

     fft: a logical indicating whether phase randomized sur-
          rogate data is generated.

amplitude: a logical indicating whether amplitude-adjusted
          surrogate data is computed.

normalized: a logical indicating whether the normalized auto
          mutual information function is computed.

   trace: a logical indicating whether additional output
          from the computation is traced.

    plot: a logical indicating whether the AMIF is plotted.

     ...: additional arguments to `plot.amif'.

     obj: an object of class `"amif"'.

  ci.col: color to plot the confidence bound.

     ...: additional arguments to `plot.acf'.

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

     To compute the AMIF, an implementation of the algorithm
     of Fraser and Swinney (1986) is used.

_V_a_l_u_e_:

     An object of class `"amif","acf"'.

_A_u_t_h_o_r_(_s_)_:

     Fraser and Swinney (1986) algorithm: The group of F. W.
     Schneider at the University of Wuerzburg, Germany:
     Authors T. M. Kruel, Institut fuer Physikalische
     Chemie, University of Wuerzburg, Germany, and K.
     Krischer, Fritz-Haber-Institut der Max-Planck-
     Gesellschaft, Berlin, Germany.

     Port to R, implementation of AMIF, and scramble device:
     A. Trapletti.

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

     C. Granger and J. L. Lin (1994): Using the Mutual
     Information Coefficient to Identify Lags in Non-Linear
     Models. Journal of Time Series Analysis 15, pp.
     371-384.

     A. M. Fraser and H. L. Swinney (1986): Independent
     Coordinates for Strange Attractors from Mutual Informa-
     tion. Physical Review A 33, pp. 1134-1140.

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

     `acf', `surrogate'

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

     n <- 1000  # Length of simulated time series

     e <- rnorm (n)  # Generate ARCH(1) process
     x <- double (n)
     x[1] <- rnorm (1)
     for (i in 2:n)
     {
       x[i] <- e[i]*sqrt(0.1+0.4*x[i-1]^2)
     }
     x <- ts(x)
     plot (x)

     # Each test takes about 3 sec on a Pentium II 300MHz

     amif (x, lag.max=5)  # i.i.d. vs. any dependence
     amif (x, lag.max=5, fft=T)  # linear vs. non-linear
     amif (x, lag.max=5, fft=T, amplitude=T)

     e <- rnorm (n)  # Generate AR(1) process
     x <- double (n)
     x[1] <- rnorm (1)
     for (i in 2:n)
     {
       x[i] <- 0.4*x[i-1]+e[i]
     }
     x <- ts(x)
     plot (x)

     amif (x, lag.max=5)  # i.i.d. vs. any dependence
     amif (x, lag.max=5, fft=T)  # linear vs. non-linear
     amif (x, lag.max=5, fft=T, amplitude=T)

