R/garch-Sim.R

In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA  02111-1307  USA


################################################################################
# FUNCTION:               SIMULATION:
#  garchSim                Simulates a GARCH/APARCH process
################################################################################


garchSim <-
    function(spec = garchSpec(), n = 100, n.start = 100,
             extended = FALSE)
{
    # A function implemented by Diethelm Wuertz

    # Description:
    #   Simulates a time series process from the GARCH family

    # Arguments:
    #   model - a specification object of class 'fGARCHSPEC' as
    #     returned by the function \code{garchSpec}:
    #     ar - a vector of autoregressive coefficients of
    #       length m for the ARMA specification,
    #     ma - a vector of moving average coefficients of
    #       length n for the ARMA specification,
    #     omega - the variance value for GARCH/APARCH
    #       specification,
    #     alpha - a vector of autoregressive coefficients
    #       of length p for the GARCH/APARCH specification,
    #     gamma - a vector of leverage coefficients of
    #       length p for the APARCH specification,
    #     beta - a vector of moving average coefficients of
    #       length q for the GARCH/APARCH specification,
    #     mu - the intercept for ARMA specification (mean=mu/(1-sum(ar))),
    #     delta - the exponent value used in the variance
    #       equation.
    #     skew - a numeric value for the skew parameter.
    #     shape - a numeric value for the shape parameter.
    #   n - an integer, the length of the series
    #   n.start - the length of the warm-up sequence to reduce the
    #       effect of initial conditions.

    # FUNCTION:

    # Specification:
    stopifnot(inherits(spec, "fGARCHSPEC"))
    model = spec@model

    # Random Seed:
    if (spec@rseed != 0) set.seed(spec@rseed)

    # Enlarge Series:
    n = n + n.start

    # Create Innovations:
    if (spec@distribution == "norm")
        z = rnorm(n)
    if (spec@distribution == "ged")
        z = rged(n, nu = model$shape)
    if (spec@distribution == "std")
        z = rstd(n, nu = model$shape)
    if (spec@distribution == "snorm")
        z = rsnorm(n, xi = model$skew)
    if (spec@distribution == "sged")
        z = rsged(n, nu = model$shape, xi = model$skew)
    if (spec@distribution == "sstd")
        z = rsstd(n, nu = model$shape, xi = model$skew)

    # Expand to whole Sample:
    delta = model$delta
    z = c(rev(spec@presample[, 1]), z)
    h = c(rev(spec@presample[, 2]), rep(NA, times = n))
    y = c(rev(spec@presample[, 3]), rep(NA, times = n))
    m = length(spec@presample[, 1])
    names(z) = names(h) = names(y) = NULL


    # Determine Coefficients:
    mu = model$mu
    ar = model$ar
    ma = model$ma
    omega = model$omega
    alpha = model$alpha
    gamma = model$gamma
    beta = model$beta
    deltainv = 1/delta

    # Determine Orders:
    order.ar = length(ar)
    order.ma = length(ma)
    order.alpha = length(alpha)
    order.beta = length(beta)

    # Iterate GARCH / APARCH Model:
    eps = h^deltainv*z
    for (i in (m+1):(n+m)) {
        h[i] =  omega +
            sum(alpha*(abs(eps[i-(1:order.alpha)]) -
                gamma*(eps[i-(1:order.alpha)]))^delta) +
            sum(beta*h[i-(1:order.beta)])
        eps[i] = h[i]^deltainv * z[i]
        y[i] = mu  +
            sum(ar*y[i-(1:order.ar)]) +
            sum(ma*eps[i-(1:order.ma)]) + eps[i]
    }

    # Sample:
    data = cbind(
        z = z[(m+1):(n+m)],
        sigma = h[(m+1):(n+m)]^deltainv,
        y = y[(m+1):(n+m)])
    rownames(data) = as.character(1:n)
    data = data[-(1:n.start),]


    # Return Values:
    from <-
        timeDate(format(Sys.time(), format = "%Y-%m-%d")) - NROW(data)*24*3600
    charvec  <- timeSequence(from = from, length.out = NROW(data))
    ans <- timeSeries(data = data[, c(3,2,1)], charvec = charvec)

    colnames(ans) <- c("garch", "sigma", "eps")
    ans <- if (extended) ans else ans[,"garch"]
    attr(ans, "control") <- list(garchSpec = spec)

    # Return Value:
    ans
}


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