GARCH Toolbox™

garchset - Create or modify GARCH specification structure

Syntax

Spec = garchset(param1,val1,param2,val2,...) Spec = garchset(OldSpec, param1,val1,...) Spec = garchset garchset

Description

Spec = garchset(param1,val1,param2,val2,...) creates a GARCH model specification structure Spec using the parameter-value pairs specified in the input argument list. Use garchget to retrieve the values of specification structure parameters.
Spec = garchset(OldSpec, param1,val1,...) modifies an existing GARCH specification structure OldSpec by changing the named parameters to the specified values. garchset returns an error if the new parameter values would create an invalid model.
Spec = garchset creates a GARCH specification structure Spec for the GARCH Toolbox™ default model. The conditional mean equation for this model is a simple constant plus additive noise. The conditional variance equation of the additive noise is a GARCH(1,1) model.
You can use this Spec as input to garchfit, but you cannot use it as input to garchinfer, garchpred, or garchsim.
garchset (with no input arguments and no output arguments) displays all parameter names (and their default values, where appropriate).

Input Arguments

`param1,` `param2,` ...	String representing a valid parameter field of the output structure `Spec`. Parameters lists the valid parameters and describes their allowed values. A parameter name needs to include only sufficient leading characters to uniquely identify the parameter. Parameter names are case insensitive.
`val1`, `val2`, ...	Value assigned to the corresponding parameter.
`OldSpec`	Existing GARCH specification structure as generated by `garchset` or `garchfit`.

Output Arguments

Spec

GARCH specification structure containing the style, orders, and coefficients (if specified) of the conditional mean and variance specifications of a GARCH model. It also contains the parameters associated with the Optimization Toolbox™ fmincon function.

Parameters

A GARCH specification structure includes these parameters. Except as noted, garchset sets all parameters you do not specify to their respective defaults.

General Parameters

Parameter	Value	Description
`Comment`	String. Default is a model summary.	User-defined summary comment. An example of the default is `'Mean: ARMAX(0, 0, ?); Variance: GARCH(1, 1)'`.
`Distribution`	`'T'` or `'Gaussian'`. Default is `'Gaussian'`.	Conditional distribution of innovations.
`DoF`	Scalar. Default = `[]`.	Degrees of freedom parameter for t distributions (must be > 2).

Conditional Mean Parameters

If you specify coefficient vectors AR and MA, but not their corresponding model orders R and M, garchset infers the values of the model orders from the lengths of the coefficient vectors.

Parameter	Value	Description
`R`	Nonnegative integer scalar. Default is `0`.	Autoregressive model order of an ARMA(R,M) model.
`M`	Nonnegative integer scalar. Default is `0`.	Moving-average model order of an ARMA(R,M) model.
`C`	Scalar coefficient. Default is `[]`.	Conditional mean constant. If `C = NaN`, `garchfit` ignores `C`, effectively fixing `C = 0`, without requiring initial estimates for the remaining parameters.
`AR`	R-element vector. Default is `[]`.	Conditional mean autoregressive coefficients that imply a stationary polynomial.
`MA`	M-element vector. Default is `[]`.	Conditional mean moving-average coefficients that imply an invertible polynomial.
`Regress`	Vector of coefficients. Default is `[]`.	Conditional mean regression coefficients.

Conditional Variance Parameters

If you specify coefficient vectors GARCH and ARCH, but not their corresponding model orders P and Q, garchset infers the values of the model orders from the lengths of the coefficient vectors.

Parameter	Value	Description
`VarianceModel`	`'GARCH'`, `'EGARCH'`, `'GJR'`, or `'Constant'`. Default is `'GARCH'`.	Conditional variance model.
`P`	Nonnegative integer scalar. `P` must be `0` if `Q` is `0`. Default is `0.`	Model order of GARCH(P,Q), EGARCH(P,Q), and GJR(P,Q) models.
`Q`	Nonnegative integer scalar. Default is `0`.	Model order of GARCH(P,Q), EGARCH(P,Q), and GJR(P,Q) models.
`K`	Scalar coefficient. Default is `[]`.	Conditional variance constant.
`GARCH`	`P`-element vector. Default is `[]`.	Coefficients related to lagged conditional variances.
`ARCH`	`Q`-element vector. Default is `[]`.	Coefficients related to lagged innovations (residuals).
`Leverage`	`Q`-element vector. Default is `[]`.	Leverage coefficients for asymmetric EGARCH(P,Q) and GJR(P,Q) models.

Equality Constraint Parameters

The garchfit function uses these parameters only during estimation. Use these parameters cautiously. The problem can experience difficulty converging if the fixed value is not well-suited to the data at hand.

Parameter	Value	Description
`FixDoF`	Logical scalar. Default is `[]`.	Equality constraint indicator for `DoF` parameter.
`FixC`	Logical scalar. Default is `[]`.	Equality constraint indicator for `C` constant.
`FixAR`	`R`-element logical vector. Default is `[]`.	Equality constraint indicator for `AR` coefficients.
`FixMA`	`M`-element logical vector. Default is `[]`.	Equality constraint indicator for `MA` coefficients.
`FixRegress`	Logical vector. Default is `[]`.	Equality constraint indicator for the `REGRESS` coefficients.
`FixK`	Logical scalar. Default is `[]`.	Equality constraint indicator for the `K` constant.
`FixGARCH`	`P`-element logical vector. Default is `[]`.	Equality constraint indicator for the `GARCH` coefficients.
`FixARCH`	`Q`-element logical vector. Default is `[]`.	Equality constraint indicator for the `ARCH` coefficients.
`FixLeverage`	`Q`-element logical vector. Default is `[]`.	Equality constraint indicator for `Leverage` coefficients.

Optimization Parameters

garchfit uses the following parameters when calling the Optimization Toolbox fmincon function during estimation.

Parameter	Value	Description
`Display`	`'on'` or `'off'`. Default is `'on'`.	Display iterative optimization information.
`MaxFunEvals`	Positive integer. Default = `(100*`number of estimated parameters`)`.	Maximum number of objective function evaluations allowed.
`MaxIter`	Positive integer. Default is `400`.	Maximum number of iterations allowed.
`TolCon`	Positive scalar. Default is `1e-007`.	Termination tolerance on the constraint violation.
`TolFun`	Positive scalar. Default is `1e-006`.	Termination tolerance on the objective function value.
`TolX`	Positive scalar. Default is `1e-006`.	Termination tolerance on parameter estimates.

Examples

Create a GARCH(1,1) model:

spec = garchset('P', 1, 'Q', 1) 
spec = 
          Comment: 'Mean: ARMAX(0, 0, ?);
         Variance: GARCH(1, 1)'
     Distribution: 'Gaussian'
                C: []
    VarianceModel: 'GARCH'
                P: 1
                Q: 1
                K: []
            GARCH: []
             ARCH: []

Change the model to a GARCH(1,2) model:

spec = garchset(spec, 'Q', 2) 
spec = 
          Comment: 'Mean: ARMAX(0, 0, ?); Variance: GARCH(1, 2)'
     Distribution: 'Gaussian'
                C: []
    VarianceModel: 'GARCH'
                P: 1
                Q: 2
                K: []
            GARCH: []
             ARCH: []

In each case, garchset displays the relevant fields in the specification structure.

Tip Use garchget to retrieve the values of individual fields.