ExtremeIndex            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 simulate time series
     with a known extremal index, and to estimate  the extremal index
     by four different kind of methods,  the blocks method, the
     reciprocal mean cluster size  method, the runs method, and the
     method of Ferro and Segers. 

     The functiona are:

       'thetaSim'          Simulates a time Series with known theta,
       'blockTheta'        Computes theta from Block Method,
       'clusterTheta'      Computes theta from Reciprocal Cluster Method,
       'runTheta'          Computes theta from Run Method,
       'ferrosegersTheta'  Computes Theta according to Ferro and Seegers,
       'exindexPlot'       Calculate and Plot Theta(1,2,3),
       'exindexesPlot'     Calculate Theta(1,2) and Plot Theta(1).

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

     ## S4 method for signature 'fTHETA':
     show(object)

     thetaSim(model = c("max", "pair"), n = 1000, theta = 0.5)

     blockTheta(x, block = 22, quantiles = seq(0.950, 0.995, length = 10),
         title = NULL, description = NULL)
     clusterTheta(x, block = 22, quantiles = seq(0.950, 0.995, length = 10),
         title = NULL, description = NULL)
     runTheta(x, block = 22, quantiles = seq(0.950, 0.995, length = 10),
         title = NULL, description = NULL)
     ferrosegersTheta(x, quantiles = seq(0.950, 0.995, length = 10),
         title = NULL, description = NULL)
         
     exindexPlot(x, block = c("monthly", "quarterly"), start = 5, end = NA, 
         doplot = TRUE, plottype = c("thresh", "K"), labels = TRUE, ...)
         
     exindexesPlot(x, block = 22, quantiles = seq(0.950, 0.995, length = 10), 
         doplot = TRUE, labels = TRUE, ...)

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

   block: [*Theta] - 
           an integer value, the block size. Currently only integer
          specified block sizes are supported. 
           [exindex*Plot] - 
           the block size. Either '"monthly"', '"quarterly"' or an
          integer value. An integer value is interpreted as the number 
          of data values in each successive block. The default value is
          '"monthly"' which correpsond for daily data to an
          approximately 22-day periods. 

description: a character string which allows for a brief description. 

  doplot: a logical, should the results be plotted? 

  labels: whether or not axes should be labelled. If set to 'FALSE'
          then user specified lables can be passed through the '"..."'
          argument. 

   model: [thetaSim] - 
           a character string denoting the name of the model. Either 
          '"max"' or '"pair"', the first representing the  maximimum
          Frechet series, and the second the paired exponential series. 

       n: [thetaSim] - 
           an integer value, the length of the time series to be
          generated. 

  object: an object of class '"fTHETA"' as returned by the functions
          '*Theta'. 

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. 

   theta: [thetaSim] - 
           a numeric value between 0 and 1 setting the value of the
          extremal index for the maximum Frechet time series. (Not used
          in the case of the paired exponential series.) 

   title: a character string which allows for a project title. 

       x: a 'timeSeries' object or any other object which can be
          transformed by the function 'as.vector' into a numeric
          vector. '"monthly"' and '"quarterly"' blocks require 'x' to
          be an object of class '"timeSeries"'. 

     ...: 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 parts of 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:

     ## Extremal Index for the right and left tails 
     ## of the BMW log returns:
        data(bmwRet)
        par(mfrow = c(2, 2), cex = 0.7)
        exindexPlot( as.timeSeries(bmwRet), block = "quarterly")
        exindexPlot(-as.timeSeries(bmwRet), block = "quarterly")   
        
     ## Extremal Index for the right and left tails 
     ## of the BMW log returns:
        exindexesPlot( as.timeSeries(bmwRet), block = 65)
        exindexesPlot(-as.timeSeries(bmwRet), block = 65)   

