rugarch (version 1.0-3)

arfimadistribution-methods: 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.par

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.

...

.

Value

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

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.

Examples

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))
	}