mle.arfima {nsarfima}

Pseudo-Maximum Likelihood Estimation of ARFIMA Model

Description

Fits an ARFIMA(p,d,q) model to a time series using a pseudo-maximum likelihood estimator. For details see Beran (1995).

Usage

mle.arfima(
  y,
  p = 1,
  q = 0,
  d.range = c(0, 1),
  start,
  incl.mean = TRUE,
  verbose = FALSE,
  method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"),
  control = list()
)

Arguments

y

Numeric vector of the time series.

p

Autoregressive order.

q

Moving average order.

d.range

Range of allowable values for fractional differencing parameter. Smallest value must be greater than -1.

start

Named vector of length 1 + p + q containing initial fit values for the fractional differencing parameter, the AR parameters, and the MA parameters (e.g. start = c(d=0.4, ar.1=-0.4, ma.1=0.3, ma.2=0.4)). If missing, automatically selected.

incl.mean

Whether or not to include a mean term in the model. The default value of TRUE is recommended unless the true mean is known and previously subtracted. Mean is returned with standard error, which may be misleading for d>=0.5.

verbose

Whether to print summary of fit.

method

Method for optim, see help(optim).

control

List of additional arguments for optim, see help(optim).

Value

A list containing:

pars	A numeric vector of parameter estimates.
std.errs	A numeric vector of standard errors on parameters.
cov.mat	Parameter covariance matrix (excluding mean).
fit.obj	optim fit object.
p.val	Ljung-Box p-value for fit.
residuals	Fit residuals.

References

Beran, J. (1995). Maximum Likelihood Estimation of the Differencing Parameter for Short and Long Memory Autoregressive Integrated Moving Average Models. Journal of the Royal Statistical Society. Series B (Methodological), 57, No. 4, 659-672. doi: 10.1111/j.2517-6161.1995.tb02054.x

See Also

mde.arfima for minimum distance estimation.

Examples

set.seed(1)
x <- arfima.sim(1000, d=0.6, ar=c(-0.4))
fit <- mle.arfima(x, p=1, incl.mean=FALSE, verbose=TRUE) 

## Fit Summary
## --------------------
## Ljung-Box p-val:  0.263 
##        sig2       d     ar.1
## est 1.09351 0.53933 -0.37582
## err 0.05343 0.04442  0.05538
##
## Correlation Matrix for ARFIMA Parameters
##         sig2       d    ar.1
## sig2  1.0000 -0.3349  0.4027
## d    -0.3349  1.0000 -0.8318
## ar.1  0.4027 -0.8318  1.0000