ScalingLawPlot            package:fBasics            R Documentation

_S_c_a_l_i_n_g _L_a_w _B_a_h_a_v_i_o_u_r

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

     Evaluates the scaling exponent of a financial  return series and
     plots the scaling law.

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

     scalinglawPlot(x, span = ceiling(log(length(x)/252)/log(2)), doplot = TRUE, 
         labels = TRUE, trace = TRUE, ...)

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

  doplot: a logical value. Should a plot be displayed? 

  labels: a logical value. Whether or not x- and y-axes should be
          automatically  labeled and a default main title should be
          added to the plot. By default 'TRUE'. 

    span: an integer value, determines for the 'qqgaussPlot' the  plot
          range, by default 5, and for the 'scalingPlot' a reasonable
          number of of points for the scaling range, by default daily
          data with 252 business days per year are assumed. 

   trace: a logical value. Should the computation be traced? 

       x: an uni- or multivariate return series of class 'timeSeries' 
          or any other object which can be transformed by the function
          'as.timeSeries()' into an object of class 'timeSeries'. 

     ...: arguments to be passed. 

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

     *Scaling Behavior:* 

      The function 'scalingPlot' plots the scaling law of financial 
     time series under aggregation and returns an estimate for the
     scaling  exponent. The scaling behavior is a very striking effect
     of the  foreign exchange market and also other markets expressing
     a regular structure for the volatility. Considering the average
     absolute return over individual data periods one finds a scaling
     power law which relates the mean volatility over given time
     intervals to the size of these intervals. The power law is in many
     cases  valid over several orders of magnitude in time. Its
     exponent   usually deviates significantly from a Gaussian random
     walk model  which implies 1/2.

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

     returns a list with the following components: 'Intercept',
     'Exponent' the scaling exponent, and 'InverseExponent' its inverse
     value.

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

     Diethelm Wuertz for the Rmetrics R-port.

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

     Taylor S.J. (1986);  _Modeling Financial Time Series_, John Wiley
     and Sons, Chichester.

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

        
     ## data - 
        # require(MASS)
        plot(SP500, type = "l", col = "steelblue", main = "SP500")
        abline(h = 0, col = "grey")

     ## scalinglawPlot -
        # Taylor Effect:
        scalinglawPlot(SP500)

