ChaoticTimeSeries          package:fSeries          R Documentation

_C_h_a_o_t_i_c _T_i_m_e _S_e_r_i_e_s _M_o_d_e_l_l_i_n_g

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

     A collection and description of functions to  investigate the
     chaotic behavior of time series  processes. Included are functions
     to simulate  different types of chaotic time series maps. 

     Chaotic Time Series Maps:

       'henonSim'     Simulates data from theHenon Map,
       'ikedaSim'     simulates data from the Ikeda Map,
       'logisticSim'  simulates data from the Logistic Map,
       'lorentzSim'   simulates data from the Lorentz Map,
       'roesslerSim'  simulates data from the Roessler Map.

     Sorry, currently are implemented only functions to simulate
     chaotic time maps.

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

     henonSim(n = 1000, n.skip = 100, parms = c(a = 1.4, b = 0.3), 
             start = runif(2), doplot = FALSE)
     ikedaSim(n = 1000, n.skip = 100, parms = c(a = 0.4, b = 6.0, c = 0.9), 
             start = runif(2), doplot = FALSE)
     logisticSim(n = 1000, n.skip = 100, parms = c(r = 4), start = runif(1), 
             doplot = FALSE)
     lorentzSim(times = seq(0, 40, by = 0.01), parms = c(sigma = 16, r = 45.92, 
             b = 4), start = c(-14, -13, 47), doplot = TRUE, ...)
     roesslerSim(times = seq(0, 100, by = 0.01), parms = c(a = 0.2, b = 0.2, c = 8.0),
             start = c(-1.894, -9.920, 0.0250), doplot = TRUE, ...)

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

n, n.skip: [henonSim][ikedaSim][logisticSim] - 
           the number of chaotic time series points to be generated and
          the  number of initial values to be skipped from the series.  

   parms: the parameter vector characterizing the chaotic map. 

   start: the vector of start values to initiate the chaotic map. 

  doplot: a logical value. Should a plot be displayed? By default
          FALSE. 

   times: [lorentzSim][roesslerSim] - 
           the sequence of time series points at which to generate the
          map.  

     ...: arguments to be passed. 

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

     All functions return invisible a vector of time series data.

_A_u_t_h_o_r(_s):

     Diethelm Wuertz for the Rmetrics R-port.

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

     Brock, W.A., Dechert W.D., Sheinkman J.A. (1987);  _A Test of
     Independence Based on the Correlation  Dimension_,  SSRI no. 8702,
     Department of Economics, University of  Wisconsin, Madison.

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

     'RandomInnovations'.

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

     ## SOURCE("fBasics.A0-SPlusCompatibility")
     ## SOURCE("fBasics.B4-TestsClass")
     ## SOURCE("fSeries.A4-TseriesTests")

     ## bdsTest -
        xmpSeries("\nNext: Brock-Dechert-Sheinkman Test for iid Series >")
        # iid Time Series:
        par(mfrow = c(3, 1))
        x = rnorm(100)
        plot(x, type = "l", main = "iid Time Series")
        bdsTest(x, m = 3)
        # Non Identically Distributed Time Series:
        x = c(rnorm(50), runif(50))
        plot(x, type = "l", main = "Non-iid Time Series")
        bdsTest(x, m = 3)  
        # Non Independent Innovations from Quadratic Map:
        x = rep(0.2, 100)
        for (i in 2:100) x[i] = 4*(1-x[i-1])*x[i-1]
        plot(x, type = "l", main = "Quadratic Map")
        bdsTest(x, m = 3)
        
     ## tnnTest -
        xmpSeries("\nNext: Teraesvirta NN test for Neglected Nonlinearity >")
        # Time Series Non-linear in "mean" regression 
        par(mfrow = c(2, 1))
        n = 1000
        x = runif(1000, -1, 1)  
        tnnTest(x)
        # Generate time series which is nonlinear in "mean"
        x[1] = 0.0
        for (i in (2:n)) {
          x[i] = 0.4*x[i-1] + tanh(x[i-1]) + rnorm (1, sd = 0.5) }
        plot(x, main = "Teraesvirta Test", type = "l")
        tnnTest(x)
        
     ## wnnTest -
        xmpSeries("\nNext: White NN test for Neglected Nonlinearity >")
        # Time Series Non-Linear in "mean" Regression
        par(mfrow = c(2, 1))
        n = 1000
        x = runif(1000, -1, 1)
        wnnTest(x)
        # Generate time series which is nonlinear in "mean"
        x[1] = 0.0
        for (i in (2:n)) {
          x[i] = 0.4*x[i-1] + tanh(x[i-1]) + rnorm (1, sd = 0.5) }
        plot(x, main = "White Test", type = "l")
        wnnTest(x)                     

