GarchFitting             package:fGarch             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 _F_i_t_t_i_n_g

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

     Estimates the parameters of an univariate GARCH process.

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

         
     garchFit(formula, data, init.rec = c("mci", "uev"), delta = 2, skew = 1, 
         shape = 4, cond.dist = c("dnorm", "dsnorm", "dged", "dsged", "dstd", "dsstd"), 
         include.mean = TRUE, include.delta = NULL, include.skew = NULL,
         include.shape = NULL, leverage = NULL, trace = TRUE,  
         algorithm = c("nlminb", "sqp", "lbfgsb", "nlminb+nm", "lbfgsb+nm"), 
         control = list(), title = NULL, description = NULL, ...)
         
     garchKappa(cond.dist = c("dnorm", "dged", "dstd", "dsnorm", "dsged", "dsstd"), 
         gamma = 0, delta = 2, skew = NA, shape = NA)

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

algorithm: a string parameter that determines the algorithm used for
          maximum  likelihood estimation. Allowed values are '"sqp"', 
          '"nlminb"', and '"bfgs"' where the first is the default
          setting. 

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

 control: control parameters, the same as used for the functions from
          'nlminb', and 'bfgs' and 'Nelder-Mead' from 'optim'. 

    data: an optional timeSeries or data frame object containing the
          variables  in the model. If not found in 'data', the
          variables are taken  from 'environment(formula)', typically
          the environment from which 'armaFit' is called. If 'data' is
          an univariate series, then the series is converted into a
          numeric vector and the name of the response in the formula
          will be neglected. 

delta, include.delta: the exponent 'delta' of the variance recursion.
          By default, this value will be fixed, otherwise the exponent
          will be estimated  together with the other model parameters
          if 'include.delta=FALSE'. 

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

 formula: formula object describing the mean and variance equation of
          the  ARMA-GARCH/APARCH model. A pure GARCH(1,1) model is
          selected  when e.g. 'formula=~garch(1,1)'. To specify for
          example an  ARMA(2,1)-APARCH(1,1) use 'formula =
          ~arma(2,1)+apaarch(1,1)'. 

   gamma: APARCH leverage parameter entering into the formula for
          calculating the expectation value. 

include.mean: this flag determines if the parameter for the mean will
          be estimated or not. If 'include.mean=TRUE' this will be the
          case, otherwise the parameter will be kept fixed durcing the
          process of parameter optimization. 

include.skew, include.shape: this flag determines if the parameters for
          the skew and shape of the conditional distribution will be
          estimated or not. If  'include.skew=TRUE' and/or
          'include.shape=TRUE' this will  be the case, otherwise the
          parameters will be kept fixed durcing  the process of
          parameter optimization. 

init.rec: a character string indicating the method how to initialize
          the  mean and varaince recursion relation.  

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

skew, shape: skewness and shape parameter of the conditional
          distribution. 

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

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

     ...: additional arguments to be passed. 

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

     'garchFit'

      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, one for the mean and the
          other one for the variance equation. 

 @method: a string denoting the optimization method, by default the 
          returneds string is "Max Log-Likelihood Estimation". 

   @data: a list with one entry named 'x', containing the data of the
          time series to be estimated, the same as given by the input
          argument 'series'. 

    @fit: a list with the results from the parameter estimation. The
          entries of the list depend on the selected algorithm, see
          below. 

@residuals: a numeric vector with the residual values. 

 @fitted: a numeric vector with the fitted values. 

    @h.t: a numeric vector with the conditional variances. 

@sigma.t: a numeric vector with the conditional variances. 

  @title: a title string. 

@description: a string with a brief description. 


     The entries of the @fit slot show the results from the
     optimization.

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

     Diethelm Wuertz for the Rmetrics R-port,
      R Core Team for the 'optim' R-port,
      Douglas Bates and Deepayan Sarkar for the 'nlminb' R-port,
      Bell-Labs for the underlying PORT Library,
      Ladislav Luksan for the underlying Fortran SQP Routine, 
      Zhu, Byrd, Lu-Chen and Nocedal for the underlying L-BFGS-B
     Routine.

_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.

     Byrd R.H., Lu P., Nocedal J., Zhu C. (1995); _A Limited Memory
     Algorithm for Bound Constrained Optimization_, SIAM Journal of
     Scientific Computing 16, 1190-1208.

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

     Nash J.C. (1990); _Compact Numerical Methods for Computers_,
     Linear Algebra and Function Minimisation, Adam Hilger.

     Nelder J.A., Mead R. (1965); _A Simplex Algorithm for Function
     Minimization_, Computer Journal 7, 308-313.

     Nocedal J., Wright S.J. (1999); _Numerical Optimization_,
     Springer, New York.

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

     ## garchSpec -
        spec = garchSpec()
        spec

     ## garchSim -
        x = garchSim(model = spec@model, n = 500)
        head(x) 

     ## garchFit - 
        # fit = garchFit(~garch(1, 1), data = x)
        # print(fit)
        ## Interactive Plot:
        ## plot(fit)
        ## Batch Plot:
        # plot(fit, which = 3)
        # summary(fit)

