APARCH Models with GEV and Stable Distributions

Description Usage Arguments Details Value Author(s) References Examples

Specifies an ARMA-GARCH or ARMA-APARCH model.

gsSpec(model = list(), presample = NULL, 
    cond.dist = c("stableS0", "stableS1", "stableS2", "gev", 
    "gat", "norm", "std", "sstd", "skstd", "ged"), 
    rseed = NULL)

`model`	a list of ARMA-GARCH/APARCH model parameters: `omega` - the coefficient of the variance equation; `alpha` - the value or vector of autoregressive coefficients; `beta` - the value or vector of variance coefficients; The values for the ARMA part are: `mu` - the mean value; `ar` - the autoregressive coefficients; `ma` - the moving average coefficients. The parameters for the conditional distributions are: `skew` - the skewness parameter; `shape` - the shape parameter.
`presample`	presample - a numeric "matrix" with 3 columns and with max(m,n,p,q) rows. The first culumn are the innovations, the second the conditional variances, and the last the time series. When the presample matrix is missing, it is constructed as [z,h,y] where z ~ Normal(0,1), h = "uev" recursion initialization described in Wuertz et al. (2009) and y = `mu`. Note that the conditional variance column can contain only strictly positive numbers and the function `gsSpec` check for invalid values.
`cond.dist`	a character string naming the conditional distribution of innovations. The package was created to accept the following distributions: `"stableS0"` (stable in S0-parameterization), `"stableS1"` (stable in S1-parameterization), `"stableS2"` (stable in S2-parameterization), `"gev"`, `"gat"` and `"skstd"` (skew Student's t from Fernandez and Steel (1998)). Other common conditional distribution (normal, Student's t, `"sstd"` (skew Student's t from fGarch package) and GED) are also allowed since they are very important for testing purposes.
`rseed`	the seed for the intitialization of the random number generator for the innovations.

This functions uses the interface of the garchSpec routine from package fGarch to simulate random values of the ARMA-GARCH/APARCH model with conditional GEV or stable distribution.

The returned value is an object of class "GEVSTABLEGARCHSPEC".

Thiago do Rego Sousa for the latest modifications
Diethelm Wuertz for the original implementation of the garchSim function from package fGarch

Wuertz, D., Chalabi, Y., with contribution from Miklovic, M., Boudt, C., Chausse, P., and others (2013). fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling, R package version 3010.82, http://CRAN.R-project.org/package=fGarch.

Wuertz, D., Chalabi, Y., Luksan, L. (2009). Parameter Estimation of ARMA Models with GARCH/ APARCH Errors: An R and SPlus SoftwareImplementation. Journal of Statistical Software, forthcoming, http://www-stat.wharton.upenn.edu/~steele/...WurtzEtAlGarch.pdf.

# stable-GARCH from Curto et al. (2009) for the DJIA dataset
spec.stable = gsSpec(model = list(mu = 0.0596, omega = 0.0061, 
alpha = 0.0497, beta = 0.9325, skew = -0.9516, shape = 1.9252), 
cond.dist = "stableS1")
sim.stable = gsSim(spec = spec.stable, n = 1000)
 
# GEV-GARCH model from Zhao et al. (2011)
spec.gev = gsSpec(model = list(mu = 0.21, a = 0.32, omega = 0.01,
alpha = 0.45, beta = 0.08, shape = 0.08), cond.dist = "gev")
sim.gev = gsSim(spec = spec.gev, n = 1000)