garchSpec               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 _S_p_e_c_i_f_i_c_a_t_i_o_n

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

     Specifies an univariate GARCH time series model.

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

     garchSpec(model = list(), presample = NULL, 
         cond.dist = c("norm", "ged", "std", "snorm", "sged", "sstd"), 
         rseed = NULL)

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

cond.dist: a character string naming the desired conditional
          distribution. Valid values are '"norm"', '"ged"', '"std"', 
          '"snorm"', '"sged"', '"sstd"'. The default value  is the
          normal distribution. 

   model: a list of GARCH model parameters: 
           'omega' - the constant coefficient of the variance equation,
          by default 1e-6; 
           'alpha' - the value or vector of autoregressive
          coefficients,  by default 0.1, specifying a model of order 1; 
           'beta' - the value or vector of variance coefficients, by
          default 0.8, specifying a model of order 1;  
           The values for the linear part are: 
           'mu' - the mean value, by default NULL; 
           'ar' - the autoregressive ARMA coefficients, by default
          NULL; 
           'ma' - the moving average ARMA coefficients, by default
          NULL.  
           The parameters for the conditional distributions are:
           'skew' - the skewness parameter (also named "xi"), by
          default 0.9, effective only for the '"dsnorm"', the
          '"dsged"', and the '"dsstd"' skewed conditional
          distributions; 
           'shape' - the shape parameter (also named "nu"), by default
          2  for the '"dged"' and '"dsged"', and by default 4 for the
          '"dstd"' and '"dsstd"' conditional distributions.

           Note, the default 'model=list()' specifies Bollerslev's 
          GARCH(1,1) model with normal conditional distributed
          innovations. 

presample: a numeric three column matrix with start values for the
          series,  for the innovations, and for the conditional
          variances. For an  ARMA(m,n)-GARCH(p,q) process the number of
          rows must be at least  max(m,n,p,q)+1, longer presamples are
          cutted. Note, all presamples are initialized by a
          normal-GARCH(p,q) process. 

   rseed: single integer argument, the seed for the intitialization of
          the random number generator for the innovations. Using the
          default value 'rseed=NULL' then the random number generation
          will be started with 'set.seed(0)'. 

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

     The function 'garchSpec' specifies a GARCH or APARCH time series
     process which we can use for simulating artificial GARCH and/or
     APARCH models. This is very useful for testing the GARCH parameter
     estimation results, since your model parameters are known and well
     specified.

     For example specifying a subet AR(5[1,5])-GARCH(2,1) model with a 
     standardized Student-t distribution with four degrees of freedom 
     will return the following printed output:


             garchSpec(model = list(ar = c(0.5,0,0,0,0.1), alpha =  
                 c(0.1, 0.1), beta = 0.75, shape = 4), cond.dist =
     "std")  

             Formula: 
              ~ ar(5) + garch(2, 1)  
             Model: 
              ar:    0.5 0 0 0 0.1  
              omega: 1e-06  
              alpha: 0.1 0.1  
              beta:  0.75  
             Distribution:   
              std  
             Distributional Parameter:  
              nu = 4  
             Presample:  
                time          z     h y  
             0     0 -0.3262334 2e-05 0  
             -1   -1  1.3297993 2e-05 0  
             -2   -2  1.2724293 2e-05 0  
             -3   -3  0.4146414 2e-05 0  
             -4   -4 -1.5399500 2e-05 0  

     The "Formula" describes the formula expression specifying the
     generating process, "Model" lists the associated model parameters,
     "Distribution" the type of the conditional distribution function
     in use, "Distributional Parmeters" lists the distributional 
     parameter (if any), and the "Presample' shows the presample input
     matrix.

     If we have specified 'presample=NULL' in the argument list,  then
     the presample is generated automatically by default as  
     norm-AR()-GARCH() process.

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

     The returned value is an object of class '"fGARCHSPEC"'.

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

     Diethelm Wuertz for the Rmetrics R-port.

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

     ## garchSpec -

        # Normal Conditional Distribution:
        spec = garchSpec()
        spec
        
        # Skewed Normal Conditional Distribution:
        spec = garchSpec(model = list(skew = 0.8), cond.dist = "snorm")
        spec
        
        # Skewed GED Conditional Distribution:
        spec = garchSpec(model = list(skew = 0.9, shape = 4.8), cond.dist = "sged")
        spec
        
     ## More specifications ...

        # Default GARCH(1,1) - uses default parameter settings
        garchSpec(model = list())
        
        # ARCH(2) - use default omega and specify alpha, set beta=0!
        garchSpec(model = list(alpha = c(0.2, 0.4), beta = 0))
        
        # AR(1)-ARCH(2) - use default mu, omega
        garchSpec(model = list(ar = 0.5, alpha = c(0.3, 0.4), beta = 0))
        
        # AR([1,5])-GARCH(1,1) - use default garch values and subset ar[.]
        garchSpec(model = list(mu = 0.001, ar = c(0.5,0,0,0,0.1)))
        
        # ARMA(1,2)-GARCH(1,1) - use default garch values
        garchSpec(model = list(ar = 0.5, ma = c(0.3, -0.3)))  
        
        # GARCH(1,1) - use default omega and specify alpha/beta
        garchSpec(model = list(alpha = 0.2, beta = 0.7))
        
        # GARCH(1,1) - specify omega/alpha/beta
        garchSpec(model = list(omega = 1e-6, alpha = 0.1, beta = 0.8))
        
        # GARCH(1,2) - use default omega and specify alpha[1]/beta[2]
        garchSpec(model = list(alpha = 0.1, beta = c(0.4, 0.4)))
        
        # GARCH(2,1) - use default omega and specify alpha[2]/beta[1]
        garchSpec(model = list(alpha = c(0.12, 0.04), beta = 0.08))
        
        # snorm-ARCH(1) - use defaults with skew Normal
        garchSpec(model = list(beta = 0, skew = 0.8), cond.dist = "snorm")
        
        # sged-GARCH(1,1) - using defaults with skew GED
        garchSpec(model = list(skew = 0.93, shape = 3), cond.dist = "sged")
        
        # Taylor Schwert GARCH(1,1) - this belongs to the family of APARCH Models
        garchSpec(model = list(delta = 1))
        
        # AR(1)-t-APARCH(2, 1) - a little bit more complex specification ...
        garchSpec(model = list(mu = 1.0e-4, ar = 0.5, omega = 1.0e-6, 
            alpha = c(0.10, 0.05), gamma = c(0, 0), beta = 0.8, delta = 1.8, 
            shape = 4, skew = 0.85), cond.dist = "sstd")

