arch |

Estimate generalized autoregressive conditional heteroskedasticity (GARCH) models.

Syntax

For a Diagonal VECH model:

system_name.arch(options) @diagvech c(arg) [arch(n, arg)] [tarch(n, arg)] [garch(n, arg)] [exog(series, arg)]

Indicate a Diagonal VECH model by using the @diagvech keyword. Follow the keyword with the constant term, c, and other optional terms to include in the variance equation: arch, garch, tarch, or exog (exogenous variable).

n indicates the order of the term, and arg indicates the type of coefficient for the term. For the exogenous variable, series indicates a series name.

Diagonal VECH Argument Options

c(arg) | where arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, “indef” (indefinite - default), or “vt” (variance target). |

arch(n, arg) | where n indicates the order of the term, and arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, or “indef” (indefinite - default). |

garch(n, arg) | where n indicates the order of the term, and arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, or “indef” (indefinite - default). |

tarch(n, arg) | where n indicates the order of the term, and arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, or “indef” (indefinite - default). |

exog(series, arg) | where series indicates a series name, and arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, or “indef” (indefinite - default). |

For example, “c(indef)” instructs EViews to use an indefinite matrix for the constant term, while “ARCH(1, fullrank)” includes a first order ARCH with a full rank matrix coefficient type.

For a Constant Conditional Correlation model:

system_name.arch(options) @ccc c(arg) [arch(n[, arg])] [tarch(n[, arg])] [garch(n[, arg])] [exog(series, arg)]

Indicate a Constant Conditional Correlation model by using the @ccc keyword. Follow the keyword with the constant term, c, and other optional terms to include in the variance equation: arch, garch, tarch, or exog (exogenous variable).

n indicates the order of the term, and arg indicates the type of coefficient for the term. For the exogenous variable, series indicates a series name.

Constant Conditional Correlation Argument Options

c(arg) | where arg may be “scalar” (default) or “vt” (variance target). |

arch(n[, arg]) | where n indicates the order of the term, and the optional arg may be “scalar” (default). |

garch(n[, arg]) | where n indicates the order of the term, and the optional arg may be “scalar” (default). |

tarch(n[, arg]) | where n indicates the order of the term, and the optional arg may be “scalar” (default). |

exog(series, arg) | where series indicates a series name, and arg may be “indiv” (individual - default) or “common”. |

For a Diagonal BEKK model:

system_name.arch(options) @diagbekk c(arg) [arch(n[, arg])] [tarch(n[, arg])] [garch(n[, arg])] [exog(series, arg)]

Indicate a Diagonal BEKK model by using the @diagbekk keyword. Follow the keyword with the constant term, c, and other optional terms to include in the variance equation: arch, garch, tarch, or exog (exogenous variable).

n indicates the order of the term, and arg indicates the type of coefficient for the term. For the exogenous variable, series indicates a series name.

Diagonal BEKK Argument Options

c(arg) | where arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, “indef” (indefinite - default), or “vt” (variance target). |

arch(n[, arg]) | where n indicates the order of the term, and the optional arg may be “diag” (diagonal - default). |

garch(n[, arg]) | where n indicates the order of the term, and the optional arg may be “diag” (diagonal - default). |

tarch(n[, arg]) | where n indicates the order of the term, and the optional arg may be “diag” (diagonal - default). |

exog(series, arg) | where series indicates a series name, and arg may be “scalar”, “diag” (diagonal), “rank1” (rank one), “fullrank”, or “indef” (indefinite - default). |

Options

General Options

tdist | Estimate the model assuming that the residuals follow a conditional Student’s t-distribution (the default is the conditional normal distribution). |

optmethod = arg | Optimization method: “bfgs” (BFGS); “newton” (Newton-Raphson), “opg” or “bhhh” (OPG or BHHH), “legacy” (EViews legacy). “bfgs” is the default for new equations. |

optstep = arg | Step method: “marquardt” (Marquardt - default); “dogleg” (Dogleg); “linesearch” (Line search). (Applicable when “optmethod=bfgs”, “optmethod=newton” or “optmethod=opg”.) |

b | Use Berndt-Hall-Hall-Hausman (BHHH) as maximization algorithm. The default is Marquardt. (Applicable when “optmethod=legacy”.) |

cov=arg | Covariance method: “ordinary” (default method based on inverse of the estimated information matrix), “huber” or “white” (Huber-White sandwich method), “bollerslev” (Bollerslev-Wooldridge method). |

covinfo = arg | Information matrix method: “opg” (OPG); “hessian” (observed Hessian), “ (Applicable when non-legacy “optmethod=” with “cov=ordinary”.) |

h | Bollerslev-Wooldridge robust quasi-maximum likelihood (QML) covariance/standard errors. (Applicable for “optmethod=legacy” when estimating assuming normal errors.) |

m=integer | Set maximum number of iterations. |

c=scalar | Set convergence criterion. The criterion is based upon the maximum of the percentage changes in the scaled coefficients. |

s | Use the current coefficient values in “C” as starting values (see also
param). |

numericderiv / ‑numericderiv | [Do / do not] use numeric derivatives only. If omitted, EViews will follow the global default. |

fastderiv / ‑fastderiv | [Do / do not] use fast derivative computation. If omitted, EViews will follow the global default. |

showopts / ‑showopts | [Do / do not] display the starting coefficient values and estimation options in the estimation output. |

coef=arg | Specify the name of the coefficient vector of a system’s variance component; the default behavior is to use the “C” coefficient vector. |

backcast=n | Backcast weight to calculate value used as the presample conditional variance. Weight needs to be greater than 0 and less than or equal to 1; the default value is 0.7. Note that a weight of 1 is equivalent to no backcasting, i.e. using the unconditional residual variance as the presample conditional variance. |

prompt | Force the dialog to appear from within a program. |

p | Print estimation results. |

Examples

system sys01

sys01.append dlog(jy)=c(1)

sys01.append dlog(bp)=c(2)

sys01.arch @diagvech c(indef) arch(1,indef) garch(1,rank1)

creates a system SYS01, appends two equations, and estimates the system using maximum likelihood with ARCH. A Diagonal VECH model is used with the constant and order 1 ARCH coefficient matrix indefinite and order 1 GARCH coefficient rank 1 matrix.

sys01.arch @diagbekk c(fullrank) arch(1) garch(1)

estimates SYS01 using a Diagonal BEKK model of order (1,1), with constant coefficient a full rank matrix.

sys01.arch(backcast=1) @ccc c arch(1) garch(1) exog(x1,indiv) exog(x2,common)

estimates a CCC model, with each variance equation GARCH(1,1) and two exogenous variables X1 and X2. The influence of X1 on each variance equation can be varying, while X2’s coefficient is the same across all variance equations. Presample uses the unconditional variance since the backcast parameter is set to one.

Cross-references

See
“ARCH and GARCH Estimation” for a discussion of ARCH models.

See also
System::makegarch and
Equation::arch.