Stata 15 help for mgarch_ccc

[TS] mgarch ccc -- Constant conditional correlation multivariate GARCH models

Syntax

mgarch ccc eq [eq ... eq] [if] [in] [, options]

where each eq has the form

(depvars = [indepvars] [, eqoptions])

options Description ------------------------------------------------------------------------- Model arch(numlist) ARCH terms for all equations garch(numlist) GARCH terms for all equations het(varlist) include varlist in the specification of the conditional variance for all equations distribution(dist [#]) use dist distribution for errors [may be gaussian (synonym normal) or t; default is gaussian] unconcentrated perform optimization on unconcentrated log likelihood constraints(numlist) apply linear constraints

SE/Robust vce(vcetype) vcetype may be oim or robust

Reporting level(#) set confidence level; default is level(95) nocnsreport do not display constraints display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Maximization maximize_options control the maximization process; seldom used from(matname) initial values for the coefficients; seldom used

coeflegend display legend instead of statistics -------------------------------------------------------------------------

eqoptions Description ------------------------------------------------------------------------- Model noconstant suppress constant term in the mean equation arch(numlist) ARCH terms garch(numlist) GARCH terms het(varlist) include varlist in the specification of the conditional variance ------------------------------------------------------------------------- You must tsset your data before using mgarch ccc; see [TS] tsset. indepvars and varlist may contain factor variables; see fvvarlist. depvars, indepvars, and varlist may contain time-series operators; see tsvarlist. by, fp, rolling, and statsby are allowed; see prefix. coeflegend does not appear in the dialog box. See [TS] mgarch ccc postestimation for features available after estimation.

Menu

Statistics > Multivariate time series > Multivariate GARCH

Description

mgarch ccc estimates the parameters of constant conditional correlation (CCC) multivariate generalized autoregressive conditionally heteroskedastic (MGARCH) models in which the conditional variances are modeled as univariate generalized autoregressive conditionally heteroskedastic (GARCH) models and the conditional covariances are modeled as nonlinear functions of the conditional variances. The conditional correlation parameters that weight the nonlinear combinations of the conditional variance are constant in the CCC MGARCH model.

The CCC MGARCH model is less flexible than the dynamic conditional correlation MGARCH model (see [TS] mgarch dcc) and varying conditional correlation MGARCH model (see [TS] mgarch vcc), which specify GARCH-like processes for the conditional correlations. The conditional correlation MGARCH models are more parsimonious than the diagonal vech MGARCH model (see [TS] mgarch dvech).

Options

+-------+ ----+ Model +------------------------------------------------------------

arch(numlist) specifies the ARCH terms for all equations in the model. By default, no ARCH terms are specified.

garch(numlist) specifies the GARCH terms for all equations in the model. By default, no GARCH terms are specified.

het(varlist) specifies that varlist be included in the specification of the conditional variance for all equations. This varlist enters the variance specification collectively as multiplicative heteroskedasticity.

distribution(dist [#]) specifies the assumed distribution for the errors. dist may be gaussian, normal, or t.

gaussian and normal are synonyms; each causes mgarch ccc to assume that the errors come from a multivariate normal distribution. # cannot be specified with either of them.

t causes mgarch ccc to assume that the errors follow a multivariate Student t distribution, and the degree-of-freedom parameter is estimated along with the other parameters of the model. If distribution(t #) is specified, then mgarch ccc uses a multivariate Student t distribution with # degrees of freedom. # must be greater than 2.

unconcentrated specifies that optimization be performed on the unconcentrated log likelihood. The default is to start with the concentrated log likelihood.

constraints(numlist) specifies linear constraints to apply to the parameter estimates.

+-----------+ ----+ SE/Robust +--------------------------------------------------------

vce(vcetype) specifies the estimator for the variance-covariance matrix of the estimator.

vce(oim), the default, specifies to use the observed information matrix (OIM) estimator.

vce(robust) specifies to use the Huber/White/sandwich estimator.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

nocnsreport; see [R] estimation options.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Maximization +-----------------------------------------------------

maximize_options: difficult, technique(algorithm_spec), iterate(#), [no]log, trace, gradient, showstep, hessian, showtolerance, tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance, and from(matname); see [R] maximize for all options except from(), and see below for information on from(). These options are seldom used.

from(matname) specifies initial values for the coefficients. from(b0) causes mgarch ccc to begin the optimization algorithm with the values in b0. b0 must be a row vector, and the number of columns must equal the number of parameters in the model.

The following option is available with mgarch ccc but is not shown in the dialog box:

coeflegend; see [R] estimation options.

Eqoptions

noconstant suppresses the constant term in the mean equation.

arch(numlist) specifies the ARCH terms in the equation. By default, no ARCH terms are specified. This option may not be specified with model-level arch().

garch(numlist) specifies the GARCH terms in the equation. By default, no GARCH terms are specified. This option may not be specified with model-level garch().

het(varlist) specifies that varlist be included in the specification of the conditional variance. This varlist enters the variance specification collectively as multiplicative heteroskedasticity. This option may not be specified with model-level het().

Examples

--------------------------------------------------------------------------- Setup . webuse stocks

Fit a VAR(1) model of stock returns on toyota, nissan and honda, allowing for ARCH(1) and GARCH(1) errors . mgarch ccc (toyota nissan honda = L.toyota L.nissan L.honda, noconstant), arch(1) garch(1)

Drop the insignificant terms from the above model and reestimate the model . mgarch ccc (toyota nissan = , noconstant) (honda = L.nissan, noconstant), arch(1) garch(1)

--------------------------------------------------------------------------- Setup . constraint 1 _b[ARCH_toyota:L.arch] = _b[ARCH_nissan:L.arch] . constraint 2 _b[ARCH_toyota:L.garch] = _b[ARCH_nissan:L.garch]

Fit a bivariate GARCH model of stock returns on toyota and nissan, constraining the two variables' ARCH coefficients to be equal, as well as their GARCH coefficients to be equal

. mgarch ccc (toyota nissan = , noconstant), arch(1) garch(1) constraints(1 2)

--------------------------------------------------------------------------- Setup . webuse acmeh

Fit a bivariate GARCH model in which the variance equations for acme and anvil follow different processes . mgarch ccc (acme = afrelated, noconstant arch(1) garch(1)) (anvil = afinputs, arch(1/2) het(L.apex))

---------------------------------------------------------------------------

Stored results

mgarch ccc stores the following in e():

Scalars e(N) number of observations e(k) number of parameters e(k_aux) number of auxiliary parameters e(k_extra) number of extra estimates added to _b e(k_eq) number of equations in e(b) e(k_dv) number of dependent variables e(df_m) model degrees of freedom e(ll) log likelihood e(chi2) chi-squared e(p) p-value for model test e(estdf) 1 if distribution parameter was estimated, 0 otherwise e(usr) user-provided distribution parameter e(tmin) minimum time in sample e(tmax) maximum time in sample e(N_gaps) number of gaps e(rank) rank of e(V) e(ic) number of iterations e(rc) return code e(converged) 1 if converged, 0 otherwise

Macros e(cmd) mgarch e(model) ccc e(cmdline) command as typed e(depvar) names of dependent variables e(covariates) list of covariates e(dv_eqs) dependent variables with mean equations e(indeps) independent variables in each equation e(tvar) time variable e(hetvars) variables included in the conditional variance equations e(title) title in estimation output e(chi2type) Wald; type of model chi-squared test e(vce) vcetype specified in vce() e(vcetype) title used to label Std. Err. e(tmins) formatted minimum time e(tmaxs) formatted maximum time e(dist) distribution for error term: gaussian or t e(arch) specified ARCH terms e(garch) specified GARCH terms e(technique) maximization technique e(properties) b V e(estat_cmd) program used to implement estat e(predict) program used to implement predict e(marginsok) predictions allowed by margins e(marginsnotok) predictions disallowed by margins e(marginsdefault) default predict() specification for margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(Cns) constraints matrix e(ilog) iteration log (up to 20 iterations) e(gradient) gradient vector e(hessian) Hessian matrix e(V) variance-covariance matrix of the estimators e(V_modelbased) model-based variance e(pinfo) parameter information, used by predict

Functions e(sample) marks estimation sample


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