sim_from_fitted {arfima}

Simulate an ARFIMA time series from a fitted arfima object.

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

sim_from_fitted(n, model, X = NULL, seed = 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.

X

The xreg matrix to add to the series, required if there is an xreg argument in model. An error will be thrown if there is a mismatch between this argument and whether model was called with a external regressor

seed

An optional seed that will be set before the simulation. If model is multimodal, a seed will be chosen randomly if not provided, and all modes will simulate a time series with said seed set.

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 from parameters, use the funtion, arfima.sim.

Value

A sample (or list of samples) 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 returned value will be a list if the fit is multimodal.

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, arfima.sim

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

sim2 <- sim_from_fitted(100, fit)

fit2 <- arfima(sim2, order = c(1, 2, 0))
fit2

set.seed(2266)
#Fairly pathological series to fit for this package
series = arfima.sim(500, model=list(phi = 0.98, dfrac = 0.46))

X = matrix(rnorm(1000), ncol = 2)
colnames(X) <- c('c1', 'c2')
series_added <- series + X%*%c(2, 5)

fit <- arfima(series, order = c(1, 0, 0), numeach = c(2, 2))
fit_X <- arfima(series_added, order=c(1, 0, 0), xreg=X, numeach = c(2, 2))

from_series <- sim_from_fitted(1000, fit)
 
fit1a <- arfima(from_series[[1]], order = c(1, 0, 0), numeach = c(2, 2))
fit1a
fit1 <- arfima(from_series[[1]], order = c(1, 0, 0))
fit1
fit2 <- arfima(from_series[[1]], order = c(1, 0, 0))
fit2
fit3 <- arfima(from_series[[1]], order = c(1, 0, 0))
fit3
fit4 <- arfima(from_series[[1]], order = c(1, 0, 0))
fit4

Xnew = matrix(rnorm(2000), ncol = 2)
from_series_X <- sim_from_fitted(1000, fit_X, X=Xnew)

fit_X1a <- arfima(from_series_X[[1]], order=c(1, 0, 0), xreg=Xnew, numeach = c(2, 2))
fit_X1a
fit_X1 <- arfima(from_series_X[[1]], order=c(1, 0, 0), xreg=Xnew)
fit_X1
fit_X2 <- arfima(from_series_X[[2]], order=c(1, 0, 0), xreg=Xnew)
fit_X2
fit_X3 <- arfima(from_series_X[[3]], order=c(1, 0, 0), xreg=Xnew)
fit_X3
fit_X4 <- arfima(from_series_X[[4]], order=c(1, 0, 0), xreg=Xnew)
fit_X4