R rugarch simulation - r

Question

I'd like to know the range of each parameter in the rugarch specification models.
For example for distribution error "nig" and model "apARCH". I'd like to know what is the range for the parameters "skew", "shape" related to the "nig" distribution and the parameters "gamma" and "delta" for the model "apARCH".
This is my code example:
varianceModel = list(model="apARCH", garchOrder=c(1,1))
meanModel = list(armaOrder=c(1,1))
distributionModel = "nig"
fixedPars = list(mu=0, ar1 = 0.1, ma1= 0.9, omega=0.001, alpha1=0.1, beta1=0.8, gamma1 = 0.01, delta = 2, shape=1.5, skew = 0.2)
spec <- ugarchspec(variance.model = varianceModel,
mean.model= meanModel, distribution.model=distributionModel,
fixed.pars=fixedPars)
path.sgarch <- ugarchpath(spec, n.sim=1000, n.start=1, m.sim=20)
Now for each of this parameters, how I can get the possible range or the "standard" parameters?

Answer 1

There doesn't seem to be a list of ranges of possible values of such parameters in the documentation of rugarch, while this introduction provides only some partial information.
Those ranges of possible values, however, are (at least should be) standard in the sense that they provide well-defined distributions and stationary models. Hence, you should be able to find all such ranges in some other sources.
However, regarding the distributions, there actually is a hidden source in rugarch that you can use---the rugarch:::.DistributionBounds function source code. For instance, it contains
if (distribution == "nig") {
skew = 0.2
skew.LB = -0.99
skew.UB = 0.99
shape = 0.4
shape.LB = 0.01
shape.UB = 25
}
meaning that the lower and upper bounds for skew are -0.99 and 0.99, respectively. To extract those numbers faster, you may use
rugarch:::.DistributionBounds("nig")[c("skew.LB", "skew.UB")]
# $skew.LB
# [1] -0.99
#
# $skew.UB
# [1] 0.99
Regarding the variance models, typically "simple" ranges, such as as -1 < gamma < 1 for APARCH, are not available/what you want, because they only allow the model to exist, but doesn't guarantee stationarity. For instance, for GARCH(1,1) to be stationary we need alpha + beta < 1; hence, we actually have higher dimensional constraints than just intervals. As I said, you may find those online.
However, ugarchpath also checks those conditions by computing persistence(spec). Now, as you can see in
getMethod("persistence", signature(object = "uGARCHspec", pars = "missing",
distribution = "missing", model = "missing",
submodel="missing"))
there is a different way to compute this persistence for each specification. For instance, for APARCH we look at
rugarch:::.persistaparch1
# function (pars, idx, distribution = "norm")
# {
# alpha = pars[idx["alpha", 1]:idx["alpha", 2]]
# beta = pars[idx["beta", 1]:idx["beta", 2]]
# gamma = pars[idx["gamma", 1]:idx["gamma", 2]]
# delta = pars[idx["delta", 1]:idx["delta", 2]]
# skew = pars[idx["skew", 1]:idx["skew", 2]]
# shape = pars[idx["shape", 1]:idx["shape", 2]]
# ghlambda = pars[idx["ghlambda", 1]:idx["ghlambda", 2]]
# ps = sum(beta) + sum(apply(cbind(gamma, alpha), 1, FUN = function(x) x[2] *
# aparchKappa(x[1], delta, ghlambda, shape, skew, distribution)))
# return(ps)
# }
and the condition is that ps < 1. Notice that
rugarch:::.persistsgarch1
# function (pars, idx, distribution = "norm")
# {
# ps = sum(pars[idx["alpha", 1]:idx["alpha", 2]]) + sum(pars[idx["beta",
# 1]:idx["beta", 2]])
# return(ps)
# }
gives exactly alpha + beta in the case of GARCH(1,1) and then ugarchpathchecks the aforementioned stationarity condition. Hence, the most straightforward thing that you can do is to check if persistence(spec) < 1 before simulating. For instance, in your example,
persistence(spec)
# [1] 0.8997927