iARFIMA {arfima}

The Fisher information matrix of an ARFIMA process

Description

Computes the approximate or (almost) exact Fisher information matrix of an ARFIMA process

Usage

iARFIMA(
  phi = numeric(0),
  theta = numeric(0),
  phiseas = numeric(0),
  thetaseas = numeric(0),
  period = 0,
  dfrac = TRUE,
  dfs = FALSE,
  exact = TRUE
)

Arguments

phi

The autoregressive parameters in vector form.

theta

The moving average parameters in vector form. See Details for differences from arima.

phiseas

The seasonal autoregressive parameters in vector form.

thetaseas

The seasonal moving average parameters in vector form. See Details for differences from arima.

period

The periodicity of the seasonal components. Must be >= 2.

dfrac

TRUE if we include the fractional d parameter, FALSE otherwise

dfs

TRUE if we include the seasonal fractional d parameter, FALSE otherwise

exact

If FALSE, calculate the approximate information matrix via psi-weights. Otherwise the (almost) exact information matrix will be calculated. See "Details".

Details

The matrices are calculated as outlined in Veenstra and McLeod (2012), which draws on many references. The psi-weights approximation has a fixed maximum lag for the weights as 2048 (to be changed to be adaptable.) The fractional difference(s) by AR/MA components have a fixed maximum lag of 256, also to be changed. Thus the exact matrix has some approximation to it. Also note that the approximate method takes much longer than the "exact" one.

The moving average parameters are in the Box-Jenkins convention: they are the negative of the parameters given by arima.

Value

The information matrix of the model.

Author(s)

JQ (Justin) Veenstra

References

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

See Also

IdentInvertQ

Examples

tick <- proc.time()
exactI <- iARFIMA(phi = c(.4, -.2), theta = c(.7), phiseas = c(.8, -.4),
	d = TRUE, dfs = TRUE, period = 12)
proc.time() - tick
tick <- proc.time()
approxI <- iARFIMA(phi = c(.4, -.2), theta = c(.7), phiseas = c(.8, -.4), 
	d = TRUE, dfs = TRUE, period = 12, exact = FALSE)
proc.time() - tick
exactI
max(abs(exactI - approxI))