mde.arfima {nsarfima}

Minimum Distance Estimation of ARFIMA Model

Description

Fits an ARFIMA(p,d,q) model to a time series using a minimum distance estimator. For details see Mayoral (2007).

Usage

mde.arfima(
  y,
  p = 1,
  q = 0,
  d.range = c(0, 1),
  start,
  lag.max = floor(sqrt(length(y))),
  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.

lag.max

Maximum lag to use when calculating the residual autocorrelations. For details see Mayoral (2007).

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.

Note

This method makes no assumptions on the distribution of the innovation series, and the innovation variance does not factor into the covariance matrix of parameter estimates. For this reason, it is not included in the results, but can be estimated from the residuals—see Mayoral (2007).

References

Mayoral, L. (2007). Minimum distance estimation of stationary and non-stationary ARFIMA processes. The Econometrics Journal, 10, 124-148. doi: 10.1111/j.1368-423X.2007.00202.x

See Also

mle.arfima for psuedo-maximum likelihood estimation.

Examples

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


## Fit Summary
## --------------------
## Ljung-Box p-val:  0.276 
##           d     ar.1
## est 0.55031 -0.39261
## err 0.03145  0.03673
##
## Correlation Matrix for ARFIMA Parameters
##           d   ar.1
## d    1.0000 0.6108
## ar.1 0.6108 1.0000