acfPlot               package:fBasics               R Documentation

_A_u_t_o_c_o_r_r_e_l_a_t_i_o_n _F_u_n_c_t_i_o_n _P_l_o_t_s

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

     Returns plots of autocorrelations including the autocorrelation
     function ACF, the partial ACF, the lagged ACF, and the Taylor
     effect plot. 

     The functions to display stylized facts are:

       'acfPlot'      autocorrelation function plot,
       'pacfPlot'     partial autocorrelation function plot,
       'lacfPlot'     lagged autocorrelation function plot,
       'teffectPlot'  Taylor effect plot.

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

     acfPlot(x, labels = TRUE, ...)
     pacfPlot(x, labels = TRUE, ...) 

     lacfPlot(x, n = 12, lag.max = 20, type = c("returns", "values"),
         labels = TRUE, ...)

     teffectPlot(x, deltas = seq(from = 0.2, to = 3, by = 0.2), lag.max = 10, 
         ymax = NA, standardize = TRUE, labels = TRUE, ...)

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

  deltas: the exponents, a numeric vector, by default ranging  from 0.2
          to 3.0 in steps of 0.2. 

  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'. 

 lag.max: maximum lag for which the autocorrelation should be 
          calculated, an integer. 

       n: an integer value, the number of lags. 

standardize: a logical value. Should the vector 'x' be standardized? 

    type: [lacf] - 
           a character string which specifies the type of the input
          series, either "returns" or series "values". In the case of 
          a return series as input, the required value series is 
          computed by cumulating the financial returns: 
          'exp(colCumsums(x))' 

       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'. 

    ymax: maximum y-axis value on plot, 'is.na(ymax)' TRUE, then the
          value is selected automatically. 

     ...: arguments to be passed. 

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

     *Autocorrelation Functions:* 

      The functions 'acfPlot' and 'pacfPlot', plot and estimate 
     autocorrelation and partial autocorrelation function. The
     functions  allow to get a first view on correlations within the
     time series.  The functions are synonyme function calls for R's
     'acf' and  'pacf' from the the 'ts' package. 

     *Taylor Effect:* 

      The "Taylor Effect" describes the fact that absolute returns of
     speculative assets have significant serial correlation over long
     lags. Even more, autocorrelations of absolute returns are
     typically greater than those of squared returns. From these 
     observations the Taylor effect states, that that the
     autocorrelations of absolute returns to the the power of 'delta', 
     'abs(x-mean(x))^delta' reach their maximum at 'delta=1'. The
     function 'teffect' explores this behaviour. A plot is created
     which shows for each lag (from 1 to 'max.lag') the 
     autocorrelations as a function of the exponent 'delta'.  In the
     case that the above formulated hypothesis is supported, all the
     curves should peak at the same value around 'delta=1'.

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

     'acfPlot', 'pacfplot', 
      return an object of class '"acf"', see 'acf'. 

     'lacfPlot' returns a list with the following two elements: 'Rho',
     the autocorrelation function, 'lagged', the lagged correlations. 

     'teffectPlot' 
      returns a numeric matrix of order 'deltas' by 'max.lag'  with the
     values of the autocorrelations.

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

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

     Ding Z., Granger C.W.J., Engle R.F. (1993);  _A long memory
     property of stock market returns and a new model_, Journal of
     Empirical Finance 1, 83.

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

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

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

