garchxAvar {garchx}

Asymptotic Coefficient Covariance

Description

Compute the asymptotic coefficient-covariance of a GARCH(q,p,r)-X model by simulation. Note that the principles of how to use the arch, garch, asym and xreg arguments are the same as those of garchx

Usage

garchxAvar(pars, arch = NULL, garch = NULL, asym = NULL,
  xreg = NULL, vcov.type = c("ordinary", "robust"),
  innovations = NULL, Eeta4 = NULL, n = 1e+06, objective.fun = 1,
  seed = NULL)

Arguments

pars

vector of parameters of length 1 or more. The first component contains the coefficient-value of the intercept, the next component(s) the ARCH-coefficient(s), and so on.

arch

NULL or integer vector with the lags of the ARCH-terms to include. Works in the same way as the arch argument in the garchx function

garch

NULL or integer vector with the lags of the GARCH-terms. Works in the same way as the garch argument in the garchx function

asym

NULL or integer vector with the lags of the asymmetry terms to include. Works in the same way as the asym argument in the garchx function

xreg

NULL, or a vector or matrix with the covariates of the model. Works in the same way as the xreg argument in the garchx function

vcov.type

character that determines the type of coefficient-covariance

innovations

NULL or a vector with the standardised innovations to use. If NULL, then the innovations are standard normal

Eeta4

numeric, the fourth moment of the innovations. If NULL, then the value is estimated internally. Note: The value of Eeta4 is only used if vcov.type = "ordinary", otherwise it is ignored

n

integer, the number of observations to use in the simulations

objective.fun

integer equal to 1 or 0 that determines the type of objective function to use, see the code of garchxObjective

seed

NULL or an integer that sets the seed (the value is passed on to set.seed. Useful for reproducibility

Value

A matrix

Author(s)

Genaro Sucarrat, http://www.sucarrat.net/

References

Christian Francq and Le Quien Thieu (2018): 'QML inference for volatility models with covariates', Econometric Theory, doi:10.1017/S0266466617000512 Christian Francq and Jean-Michel Zakoian (2019): 'GARCH Models', 2nd Edition, Wiley

See Also

garchx, garchxSim, vcov.garchx

Examples

##asymptotic coefficient-covariance of a garch(1,1)
##note: the estimate is rough, since n is small
intercept <- 0.2
alpha <- 0.1
beta <- 0.8
pars <- c(intercept, alpha, beta)
seed <- 123 #for reproducibility
garchxAvar(pars, arch=1, garch=1, n=10000, seed=seed)