R: function: ARFIMA Parameter Distribution via Simulation

arfimadistribution-methods {rugarch}

R Documentation

function: ARFIMA Parameter Distribution via Simulation

Description

Method for simulating and estimating the parameter distribution from an ARFIMA models as well as the simulation based consistency of the estimators given the data size.

Usage

arfimadistribution(fitORspec, n.sim = 2000, n.start = 1, m.sim = 100, 
recursive = FALSE, recursive.length = 6000, recursive.window = 1000, 
prereturns = NA, preresiduals = NA, rseed = NA, 
custom.dist = list(name = NA,  distfit = NA, type = "z"), mexsimdata = NULL, 
fit.control = list(), solver = "solnp", solver.control = list(), 
parallel = FALSE, parallel.control = list(pkg = c("multicore", "snowfall"), 
cores = 2), ...)

Arguments

`fitORspec`	Either an ARFIMA fit object of class `ARFIMAfit` or alternatively an ARFIMA specification object of class `ARFIMAspec` with valid parameters supplied via the `fixed.pars` argument in the specification.
`n.sim`	The simulation horizon.
`n.start`	The burn-in sample.
`m.sim`	The number of simulations.
`recursive`	Whether to perform a recursive simulation on an expanding window.
`recursive.length`	If `recursive` is TRUE, this indicates the final length of the simulation horizon, with starting length `n.sim`.
`recursive.window`	If `recursive` is TRUE, this indicates the increment to the expanding window. Together with `recursive.length`, it determines the total number of separate and increasing length windows which will be simulated and fitted.
`prereturns`	Allows the starting return data to be provided by the user.
`preresiduals`	Allows the starting residuals to be provided by the user.
`rseed`	Optional seeding value(s) for the random number generator.
`custom.dist`	Optional density with fitted object from which to simulate.
`mexsimdata`	Matrix of simulated external regressor-in-mean data. If the fit object contains external regressors in the mean equation, this must be provided.
`solver`	One of either “nlminb” or “solnp”.
`solver.control`	Control arguments list passed to optimizer.
`fit.control`	Control arguments passed to the fitting routine (as in the `arfimafit` method).
`parallel`	Whether to make use of parallel processing on multicore systems.
`parallel.control`	The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S), and the number of cores to make use of.
`...`	.

Details

This method facilitates the simulation and evaluation of the uncertainty of ARFIMA model parameters. The recursive option also allows the evaluation of the simulation based consistency (in terms of sqrt(N) ) of the parameters as the length (n.sim) of the data increases, in the sense of the root mean square error (rmse) of the difference between the simulated and true (hypothesized) parameters.
This is an expensive function, particularly if using the recursive option, both on memory and CPU resources, performing many re-fits of the simulated data in order to generate the parameter distribution.

Value

A ARFIMAdistribution object containing details of the ARFIMA simulated parameters distribution.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
spec = arfimaspec( mean.model = list(armaOrder = c(2,2), include.mean = TRUE, 
arfima = FALSE), distribution.model = "norm", fixed.pars = list(ar1=0.6, 
ar2=0.21, ma1=-0.7, ma2=0.3, mu = 0.02, sigma = 0.02))
dist = arfimadistribution(spec, n.sim = 2000, n.start = 100, m.sim = 100, 
recursive = TRUE, recursive.length = 10000, recursive.window = 1000)
# slots:
slotNames(dist)
# methods:
# summary
show(dist)
# as.data.frame(...., window, which=c("rmse", "stats", "coef", "coefse"))
# default
as.data.frame(dist)

as.data.frame(dist, window = 1, which = "rmse")
as.data.frame(dist, window = 1, which = "stats")
as.data.frame(dist, window = 1, which = "coef")
as.data.frame(dist, window = 1, which = "coefse")


as.data.frame(dist, window = 8, which = "rmse")
as.data.frame(dist, window = 8, which = "stats")
as.data.frame(dist, window = 8, which = "coef")
as.data.frame(dist, window = 8, which = "coefse")


# create some plots
# 
nwindows = dist@dist$details$nwindows
# 2000/3000/4000/5000/6000/7000/8000/9000/10000

# expected reduction factor in RMSE for sqrt(N) consistency
expexcted.rmsegr = sqrt(2000/seq(3000,10000,by=1000))

# actual RMSE reduction
actual.rmsegr = matrix(NA, ncol = 8, nrow = 6)
rownames(actual.rmsegr) = c("mu", "ar1", "ar2", "ma2", "ma2", "sigma")
# start at 2000 (window 1)
rmse.start = as.data.frame(dist, window = 1, which = "rmse")
for(i in 2:nwindows) actual.rmsegr[,i-1] = as.numeric(as.data.frame(dist, 
window = i, which = "rmse")/rmse.start)
par(mfrow = c(2,3))
for(i in 1:6){
	plot(seq(3000,10000,by=1000),actual.rmsegr[i,], type = "l", lty = 2, 
	ylab = "RMSE Reduction", xlab = "N (sim)",main = rownames(actual.rmsegr)[i])
	lines(seq(3000,10000,by=1000), expexcted.rmsegr, col = 2)
	legend("topright", legend = c("Actual", "Expected"), col = 1:2, bty = "m", 
	lty = c(2,1))
	}

## End(Not run)

[Package rugarch version 1.0-10 Index]