rugarch (version 1.2-2)

ugarchspec-methods: function: Univariate GARCH Specification

Description

Method for creating a univariate GARCH specification object prior to fitting.

Usage

ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1), 
submodel = NULL, external.regressors = NULL, variance.targeting = FALSE), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE, archm = FALSE, 
archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE), 
distribution.model = "norm", start.pars = list(), fixed.pars = list(), ...)

Arguments

variance.model

List containing the variance model specification: model Valid models (currently implemented) are sGARCH, fGARCH, eGARCH, gjrGARCH, apARCH and iGAR

mean.model

List containing the mean model specification: armaOrder The autoregressive (ar) and moving average (ma) orders (if any). include.mean Whether to include the mean. archm Whether to include ARCH volatility in the mean

distribution.model

The conditional density to use for the innovations. Valid choices are norm for the normal distibution, snorm for the skew-normal distribution, std for the student-t, sstd for the skew

start.pars

List of staring parameters for the optimization routine. These are not usually required unless the optimization has problems converging.

fixed.pars

List of parameters which are to be kept fixed during the optimization. It is possible that you designate all parameters as fixed so as to quickly recover just the results of some previous work or published work. The optional argument fixed.se

...

.

Value

• A uGARCHspec object containing details of the GARCH specification.

Details

The specification allows for a wide choice in univariate GARCH models, distributions, and mean equation modelling. For the fGARCH model, this represents Hentschel's omnibus model which subsumes many others. For the mean equation, ARFIMAX is fully supported in fitting, forecasting and simulation. There is also an option to multiply the external regressors by the conditional standard deviation, which may be of use for example in calculating the correlation coefficient in a CAPM type setting. The iGARCH implements the integrated GARCH model. For the EWMA model just set omega to zero in the fixed parameters list. The asymmetry term in the rugarch package, for all implemented models, follows the order of the arch parameter alpha. Variance targeting, referred to in Engle and Mezrich (1996), replaces the intercept omega in the variance equation by 1 minus the persistence multiplied by the unconditional variance which is calculated by its sample counterpart in the squared residuals during estimation. In the presence of external regressors in the variance equation, the sample average of the external regresssors is multiplied by their coefficient and subtracted from the variance target. In order to understand which parameters can be entered in the start.pars and fixed.pars optional arguments, the list below exposes the names used for the parameters across the various models:(note that when a parameter is followed by a number, this represents the order of the model. Just increment the number for higher orders, with the exception of the component sGARCH permanent component parameters which are fixed to have a lag-1 autoregressive structure.):

• Mean Model
  • constant:mu
  • AR term:ar1
  • MA term:ma1
  • ARCH-in-mean:archm
  • exogenous regressors:mxreg1
  • arfima:arfima
• Distribution Model
  • skew:skew
  • shape:shape
  • ghlambda:lambda (for GHYP distribution)
• Variance Model (common specs)
  • constant:omega
  • ARCH term:alpha1
  • GARCH term:beta1
  • exogenous regressors:vxreg1
• Variance Model (GJR, EGARCH)
  • assymetry term:gamma1
• Variance Model (APARCH)
  • assymetry term:gamma1
  • power term:delta
• Variance Model (FGARCH)
  • assymetry term1 (rotation):eta11
  • assymetry term2 (shift):eta21
  • power term1(shock):delta
  • power term2(variance):lambda
• Variance Model (csGARCH)
  • permanent component autoregressive term (rho):eta11
  • permanent component shock term (phi):eta21
  • permanent component intercept:omega
  • transitory component ARCH term:alpha1
  • transitory component GARCH term:beta1

Examples

# a standard specification
spec1 = ugarchspec()
spec1
# an example which keep the ar1 and ma1 coefficients fixed:
spec2 = ugarchspec(mean.model=list(armaOrder=c(2,2), 
fixed.pars=list(ar1=0.3,ma1=0.3)))
spec2
# an example of the EWMA Model
spec3 = ugarchspec(variance.model=list(model="iGARCH", garchOrder=c(1,1)), 
		mean.model=list(armaOrder=c(0,0), include.mean=TRUE),  
		distribution.model="norm", fixed.pars=list(omega=0))