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.
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,
...
)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.
The number of points to be generated.
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.
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.
The desired variance for the innovations of the series.
The distribution of the innovations. Any distribution
recognized by R is possible
The theoretical mean of the series before integration (if integer integration is done)
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.
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.
JQ (Justin) Veenstra
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.
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.
arfima, sim_from_fitted
set.seed(6533)
sim <- arfima.sim(1000, model = list(phi = .2, dfrac = .3, dint = 2))
fit <- arfima(sim, order = c(1, 2, 0))
fit
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