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.

```
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(),
cluster = NULL, ...)
```

fitORspec

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).

cluster

A cluster object created by calling `makeCluster`

from the parallel
package. If it is not NULL, then this will be used for parallel estimation.

...

.

A `'>ARFIMAdistribution`

object containing details of the
ARFIMA simulated parameters distribution.

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.