ExtremeIndexPlots         package:fExtremes         R Documentation

_E_x_t_r_e_m_a_l _I_n_d_e_x _E_s_t_i_m_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     A collection and description of functions to compute  the extremal
     index by three different kind of methods,  the blocks method, the
     reciprocal mean cluster size  method, and the runs method.  

     The functiona are:

       'exindexPlot'    Calculate and Plot Theta(1,2,3),
       'exindexesPlot'  Calculate Theta(1,2) and Plot Theta(1).

_U_s_a_g_e:

     exindexPlot(x, block = "month", start = 5, end = NA, plottype = c("thresh", 
         "K"), labels = TRUE, autoscale = TRUE, ...)
         
     exindexesPlot(x, block = 20, quantiles = seq(0.990, 0.999, 0.001), 
         doplot = TRUE, ...)

_A_r_g_u_m_e_n_t_s:

autoscale: [exindexPlot] - 
           whether or not plot should be automatically scaled; if not, 
          'xlim' and 'ylim' graphical parameters may be entered. 

   block: the block size. A numeric value is interpreted as the number
          of  data values in each successive block. All the data is
          used, so the last block may not contain 'block' 
          observations. If the 'x' has a 'times' attribute containing
          (in an  object of class '"POSIXct"', or an object that can be
          converted to that class; see 'as.POSIXct') the times/dates of
          each observation, then 'block' may instead take the character
          values '"month"', '"quarter"', '"semester"' or '"year"'.
          Note, 'exindexPlot' supports both numeric and character
          input, 'exindexPlot' supports only numeric input. By default,
          monthly blocks or 20-day blocks are used which are  thought
          for daily data records. 

  doplot: [exindexesPlot] - 
           a logical, should the results be plotted? 

  labels: [exindexPlot] - 
           whether or not axes should be labelled. 

plottype: [exindexPlot] - 
           whether plot is to be by increasing threshold ('thresh')  or
          increasing K value ('K'). 

quantiles: [exindexesPlot] - 
           a numeric vector of quantile values. 

start, end: [exindexPlot] - 
           'start' is the lowest value of 'K' at which to plot  a
          point, and 'end' the highest value; 'K' is the number of
          blocks in which a specified threshold is exceeded. 

       x: a numeric vector, note raw values are required, not block
          maxima. 

     ...: additional arguments passed to the plot function. 

_V_a_l_u_e:

     'exindexPlot' 
      returns a data frame of results with the  following columns: 'N',
     'K', 'un', 'theta2', and 'theta'. A plot with 'K' on the lower
     x-axis and threshold Values on the upper x-axis versus the
     extremal index is displayed.

     'exindexesPlot' 
      returns a data.frame with four columns:  'thresholds', 'theta1',
     'theta2', and 'theta3'. A plot with quantiles on the x-axis and
     versus the extremal indexes is displayed.

_A_u_t_h_o_r(_s):

     Alexander McNeil, for the 'exindexPlot' function, and 
      Diethelm Wuertz for the 'exindexesPlot' function.

_R_e_f_e_r_e_n_c_e_s:

     Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); _Modelling
     Extremal Events_,  Springer. Chapter 8, 413-429.

_S_e_e _A_l_s_o:

     'hillPlot', 'gevFit'.

_E_x_a_m_p_l_e_s:

     ## SOURCE("fExtremes.55A-ExtremeIndex")

     ## Extremal Index for the right and left tails 
     ## of the BMW log returns:
        xmpExtremes("\nStart: Plot the Extremal Index >")
        data(bmw)
        par(mfrow = c(2, 2), cex = 0.7)
        exindexPlot( bmw, block = "quarter")
        exindexPlot(-bmw, block = "quarter")   
        
     ## Extremal Index for the right and left tails 
     ## of the BMW log returns:
        xmpExtremes("\nNext: Investigate Tail Depth Dependence >")
        data(bmw)
        exindexesPlot( bmw, block = 65)
        exindexesPlot(-bmw, block = 65)   

