GARCH Toolbox

garchset

Create or modify GARCH specification structure

Syntax

• garchset
  Spec = garchset
  Spec = garchset('Parameter1', Value1, 'Parameter2', Value2, ...) 
  Spec = garchset(OldSpec, 'Parameter1', Value1, ...)
  

Arguments

Parameter1, Parameter2, ...	String representing the name of a valid parameter field of the output specification structure Spec. Table 3-1, GARCH Specification Parameters below lists the valid parameters. The GARCH Toolbox ignores case for parameter names.
Value1, Value2, ...	Value assigned to the corresponding Parameter.
OldSpec	(optional) Existing GARCH specification structure. Fields of the structure were previously generated by calling garchset or garchfit.

Description

garchset provides the main user interface for specifying a GARCH model, and is the preferred method for creating and modifying GARCH specification structures. Use garchget to retrieve the values of specification structure parameters.

garchset (with no input arguments and no output arguments) displays all parameter names and the default values where appropriate.

Spec = garchset creates a GARCH specification structure Spec with all fields set to their default settings. This default GARCH specification structure models an observed univariate return series as a constant, C, plus GARCH(1,1) conditionally Gaussian innovations. The C + GARCH(1,1) model is the default model of the GARCH Toolbox. You can use this Spec as input to garchfit, but it is invalid as input to garchpred or garchsim.

Spec = garchset('Parameter1', Value1, 'Parameter2', Value2, ...) creates a GARCH specification structure Spec using the parameter/value pairs specified in the input argument list. The Parameter part of the pair must be a valid GARCH specification structure field. garchset assigns the Value part of the pair to its paired Parameter field. If you specify coefficient vectors (AR, MA, GARCH, ARCH) but not their corresponding model orders (R, M, P, Q), garchset infers the values of the model orders from the lengths of the coefficient vectors. In all other cases, garchset sets all parameters you do not specify to their respective defaults. A parameter name needs to include only sufficient leading characters to uniquely identify the parameter.

Spec = garchset(OldSpec, 'Parameter1', Value1, ...) modifies an existing GARCH specification structure, OldSpec, by changing the named parameters to the specified values.

Spec	GARCH specification structure. This structure contains the orders and coefficients (if specified) of the conditional mean and variance specifications of a GARCH model. It also contains the parameters associated with the function fmincon in the MATLAB Optimization Toolbox.

A GARCH specification structure includes the parameters shown in Table 3-1, GARCH Specification Parameters.

Table 3-1: GARCH Specification Parameters  

Parameter	Description	Possible Values
Comment	User-defined summary comment	String. The default lists expressions for the mean and variance models derived from the current values of R, M, P, and Q. For example, 'Mean: ARMAX(0,0,?); Variance: GARCH(1,1)'. If you explicitly specify a comment, the toolbox does not overwrite it.
R	Auto-regressive component of the conditional mean model order of an ARMA(R,M) model	Nonnegative integer scalar. Default = 0.
M	Moving average component of the conditional mean model order of an ARMA(R,M) model	Nonnegative integer scalar. Default = 0.
P	GARCH component of the conditional variance model order of an GARCH(P,Q) model	Nonnegative integer scalar. P must be 0 if Q is 0. Default = 0.
Q	ARCH component of the conditional variance model order of an GARCH(P,Q) model	Nonnegative integer scalar. Default = 0.
Distribution	Conditional distribution of innovations	String. The only valid value is 'Gaussian'.
C	Conditional mean constant	Scalar coefficient. Default = [].
AR	Conditional mean auto-regressive coefficients	Vector of R coefficients of lagged returns. Default = [].
MA	Conditional mean moving average coefficients	Vector of M coefficients of lagged innovations. Default = [].
Regress	Conditional mean regression coefficients	Vector of coefficients. Default = [].
K	Conditional variance constant	Positive scalar coefficient. Default = [].
GARCH	Conditional variance coefficients for lagged variances	Vector of P nonnegative coefficients. Default = [].
ARCH	Conditional variance coefficients for lagged squared residuals	Vector of Q nonnegative coefficients. Default = [].
FixC	Equality constraint indicator for C coefficient of the conditional mean	Boolean scalar. Default = 0.
FixAR	Equality constraint indicator for AR coefficients of the conditional mean	Boolean vector. Default = [0, 0, ..., 0].
FixMA	Equality constraint indicator for MA coefficients of the conditional mean	Boolean vector. Default = [0, 0, ..., 0].
FixRegress	Equality constraint indicator for the REGRESS coefficients of the conditional mean	Boolean vector. Default = [0, 0, ..., 0].
FixK	Equality constraint indicator for the K coefficient of the conditional variance	Boolean scalar. Default = 0.
FixGARCH	Equality constraint indicator for the GARCH coefficients of the conditional variance	Boolean vector. Default = [0, 0, ..., 0].
FixARCH	Equality constraint indicator for the ARCH coefficients of the conditional variance	Boolean vector. Default = [0, 0, ..., 0].
Display	Display flag for iterative optimization information	String. Valid values are on (default) and off.
MaxFunEvals	Maximum number of log-likelihood objective function evaluations allowed in the estimation process	Positive integer. Default = (100 * number of parameters in the model). For a Gaussian distribution, this is 100 * (2 + R + M + Nx + P + Q) where Nx is the number of explanatory variables in the regression component of the conditional mean.
MaxIter	Maximum number of iterations allowed in the estimation process	Positive integer. Default = 400.
TolCon	Termination tolerance on constraint violation	Positive scalar. Default = 1e-006.
TolFun	Termination tolerance on the objective function value	Positive scalar. Default = 1e-006.
TolX	Termination tolerance on parameter estimates	Positive scalar. Default = 1e-006.

Example

This example creates a GARCH(1,1) model and prints the specification structure. The nested Optimization structure, shown in the printed specification structure, contains the Display, MaxFunEvals, MaxIter, TolCon, TolFun, and TolX parameters. Use garchget to retrieve the values of these parameters.

• spec = garchset('P',1,'Q',1)   % Create a GARCH(P=1,Q=1) model.
  
  spec = 
  
           Comment: 'Mean: ARMAX(0,0,?); Variance: GARCH(1,1)'
                 R: 0
                 M: 0
                 P: 1
                 Q: 1
      Distribution: 'Gaussian'
                 C: []
                AR: []
                MA: []
           Regress: []
                 K: []
             GARCH: []
              ARCH: []
              FixC: []
             FixAR: []
             FixMA: []
        FixRegress: []
              FixK: []
          FixGARCH: []
           FixARCH: []
      Optimization: [1x1 struct]
  
  spec = garchset(spec,'Q',2)    % Change it to a GARCH(P=1,Q=2)
                                 % model.
  spec = 
  
           Comment: 'Mean: ARMAX(0,0,?); Variance: GARCH(1,2)'
                 R: 0
                 M: 0
                 P: 1
                 Q: 2
      Distribution: 'Gaussian'
                 C: []
                AR: []
                MA: []
           Regress: []
                 K: []
             GARCH: []
              ARCH: []
              FixC: []
             FixAR: []
             FixMA: []
        FixRegress: []
              FixK: []
          FixGARCH: []
           FixARCH: []
      Optimization: [1x1 struct]
  

See Also
garchfit, garchget, garchpred, garchsim

optimset (in the online MATLAB Function Reference)

garchpred

garchsim