GarchModelling            package:fSeries            R Documentation

_U_n_i_v_a_r_i_a_t_e _G_A_R_C_H _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  simulate artificial
     ARCH time series processes,  to fit the parameters of univariate
     time series  to ARCH models, to perform a diagnostic analysis of 
     the fit, and to predict future values of the time  series. 

     The family of GARCH time series models includes the following 
     processes:

       'garch'   generalized AR conditional heteroskedastic models,
       'aparch'  asymmetretic power ARCH models.

     *Note:* This collection is still under a complete reconstruction.

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

     garchSpec(model = list(omega = 1.0e-6, alpha = 0.1, beta = 0.8), 
             presample = NULL, cond.dist = c("rnorm", "rged", "rstd", "rsnorm", 
             "rsged", "rsstd"))
     ## S3 method for class 'garchSpec':
     print(x, ...)

     garchSim(model = list(omega = 1.0e-6, alpha = 0.1, beta = 0.8), n = 100, 
             presample = NULL, cond.dist = c("rnorm", "rged", "rstd", "rsnorm", 
             "rsged", "rsstd"))

     garchFit(formula.mean = ~arma(0, 0), formula.var = ~garch(1, 1), 
             series = x, presample =  NULL, 
             cond.dist = c("dnorm", "dged", "dstd", "dsnorm", "dsged", "dsstd"), 
             symmetric = TRUE, trace = TRUE, title = NULL, description = NULL, ...)
     ## S3 method for class 'fGARCH':
     print(x, ...)
     ## S3 method for class 'fGARCH':
     plot(x, ...)
     ## S3 method for class 'fGARCH':
     summary(object, ...)

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

cond.dist: [garchSpec, garchSim, garchFit] - 
           a character string naming the desired conditional
          distribution. Valid values are '"dnorm"', '"dged"', '"dstd"',
           '"dsnorm"', '"dsged"', '"dsstd"'. The default value  is the
          normal distribution. 

description: [garchFit] - 
           a character string which allows for a brief description.  

formula.mean, formula.var: [garchFit] - 
           two formula objects describing the mean and variance
          equation of the ARMA-GARCH/APARCH model. By default a pure
          GARCH(1,1) mode is selected, this means:
          'formula.mean=~arma(0,0)',  and 'formula.var=~garch(1,1)'. To
          specify for example an  APARCH(1,1) use:
          'formula.var=~apaarch(1,1)' 

   model: [garchSpec, garchSim] - 
           List of GARCH model parameters: 
           'omega' - the constant coefficient of the variance equation; 
           'alpha' - the vector of autoregressive coefficients; 
           'beta' - the vector of variance coefficients; 
           Further Optional Values: 
           'mu' - the mean value; 
           'ar' - the autoregressive ARMA coefficients; 
           'ma' - the moving average ARMA coefficients; 

           The default model is Bollerslev's GARCH(1,1) model. 

       n: [garchSim] - 
           length of output series, an integer value. An integer value,
          by default 'n=100'. 

  object: [summary] - 
           an object of class 'fGARCH' as returned from the function
          'garchFit()'. 

presample: a numeric three column matrix with start values for the
          series,  innovations, and conditional variances. For an
          ARMA(m,n)-GARCH(p,q) process the number of rows must be at
          least max(m,n,p,q), longer  presamples are cutted. 

  series: [garchFit] - 
           a numeric vector or univariate 'timeSeries' object to be 
          fitted. By default 'series=x'. 

symmetric: a logical flag for APARCH models. Should the model be
          leveraged? By default 'symmetric=TRUE'. 

   title: [garchFit] - 
           a character string which allows for a project title. 

   trace: [garchFit] - 
           a logical flag. Should the optimization process of fitting
          the model parameters be printed. By default 'trace=TRUE'. 

       x: [print][plot]  - 
           either an object of class 'garchSpec' for printing
          specification structures, or an object of class 'fGARCH' for
          printing fitted GARCH/APARCH models or plotting results from
          the diagnostic analysis of fitted models. 

     ...: additional arguments to be passed. 

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

     *Parameter Estimation:* 

      'garchFit' uses the 'nlminb()' optimizer to find the maximum
     likelihood estimates.

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

     'garchSpec'

      returns a S4 object of class 'fGARCH' with the following slots:

   @call: the call of the 'garch' function. 

@formula: a list with two formula entries for the mean and variance 
          equation. 

  @model: a list with the model parameters. 

@presample: a numeric matrix with presample values. 

@distribution: a character string with the name of the conditional
          distribution. 

   @call: the call of the 'garch' function. 

@formula: a list with two formula entries for the mean and variance 
          equation. 

 @method: a string denoting the optimization method. 

    @fit: a list with the results from the parameter estimation. 

@residuals: a numeric vector with the residual values. 

@fitted.values: a numeric vector with the fitted values. 

  @title: a title string. 

@description: a string with a brief description. 

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

     Diethelm Wuertz for the Rmetrics R-port.

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

     ATT (1984); _PORT Library Documentation_, 
     http://netlib.bell-labs.com/netlib/port/.

     Bera A.K., Higgins M.L. (1993); _ARCH Models: Properties,
     Estimation and Testing_, J. Economic Surveys 7, 305-362.

     Bollerslev T. (1986); _Generalized Autoregressive Conditional
     Heteroscedasticity_, Journal of Econometrics 31, 307-327.

     Engle R.F. (1982); _Autoregressive Conditional Heteroscedasticity
     with Estimates  of the Variance of United Kingdom Inflation_,
     Econometrica 50, 987-1008.

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

     ## SOURCE("fSeries1.34C-GarchModelling")
     ## Not run: 
     #       garchSpec -
     #   garchSim - 
     #       garchFit -

         # For examples we refer to: demo/xmpDWChapter34.R ...
     ## End(Not run)

