arfima.sim {arfima}

Simulate an ARFIMA time series.

Description

This function simulates an long memory ARIMA time series, with one of fractionally differenced white noise (FDWN), fractional Gaussian noise (FGN), power-law autocovariance (PLA) noise, or short memory noise and possibly seasonal effects.

Usage

arfima.sim(
  n,
  model = list(phi = numeric(0), theta = numeric(0), dint = 0, dfrac = numeric(0), H =
    numeric(0), alpha = numeric(0), seasonal = list(phi = numeric(0), theta = numeric(0),
    dint = 0, period = numeric(0), dfrac = numeric(0), H = numeric(0), alpha =
    numeric(0))),
  useC = 3,
  sigma2 = 1,
  rand.gen = rnorm,
  muHat = 0,
  zinit = NULL,
  innov = NULL,
  ...
)

Arguments

n

The number of points to be generated.

model

The model to be simulated from. The phi and theta arguments should be vectors with the values of the AR and MA parameters. Note that Box-Jenkins notation is used for the MA parameters: see the "Details" section of arfima. The dint argument indicates how much differencing should be required to make the process stationary. The dfrac, H, and alpha arguments are FDWN, FGN and PLA values respectively; note that only one (or none) of these can have a value, or an error is returned. The seasonal argument is a list, with the same parameters, and a period, as the model argument. Note that with a seasonal model, we can have mixing of FDWN/FGN/HD noise: one in the non-seasonal part, and the other in the seasonal part.

useC

How much interfaced C code to use: an integer between 0 and 3. The value 3 is strongly recommended. See the "Details" section of arfima.

sigma2

The desired variance for the innovations of the series.

rand.gen

The distribution of the innovations. Any distribution recognized by R is possible

muHat

The theoretical mean of the series before integration (if integer integration is done)

zinit

Used for prediction; not meant to be used directly. This allows a start of a time series to be specified before inverse differencing (integration) is applied.

innov

Used for prediction; not meant to be used directly. This allows for the use of given innovations instead of ones provided by rand.gen.

...

Other parameters passed to the random variate generator; currently not used.

Details

A suitably defined stationary series is generated, and if either of the dints (non-seasonal or seasonal) are greater than zero, the series is integrated (inverse-differenced) with zinit equalling a suitable amount of 0s if not supplied. Then a suitable amount of points are taken out of the beginning of the series (i.e. dint + period * seasonal dint = the length of zinit) to obtain a series of length n. The stationary series is generated by calculating the theoretical autovariance function and using it, along with the innovations to generate a series as in McLeod et. al. (2007). Note: if you would like to fit a function from a fitted arfima model, the function sim_from_fitted can be used.

Value

A sample from a multivariate normal distribution that has a covariance structure defined by the autocovariances generated for given parameters. The sample acts like a time series with the given parameters.

Author(s)

JQ (Justin) Veenstra

References

McLeod, A. I., Yu, H. and Krougly, Z. L. (2007) Algorithms for Linear Time Series Analysis: With R Package Journal of Statistical Software, Vol. 23, Issue 5

Veenstra, J.Q. Persistence and Antipersistence: Theory and Software (PhD Thesis)

P. Borwein (1995) An efficient algorithm for Riemann Zeta function Canadian Math. Soc. Conf. Proc., 27, pp. 29-34.

See Also

arfima, sim_from_fitted

Examples

set.seed(6533)
sim <- arfima.sim(1000, model = list(phi = .2, dfrac = .3, dint = 2))

fit <- arfima(sim, order = c(1, 2, 0))
fit