IdentInvertQ {arfima}

Checks invertibility, stationarity, and identifiability of a given set of parameters

Description

Computes whether a given long memory model is invertible, stationary, and identifiable.

Usage

IdentInvertQ(
  phi = numeric(0),
  theta = numeric(0),
  phiseas = numeric(0),
  thetaseas = numeric(0),
  dfrac = numeric(0),
  dfs = numeric(0),
  H = numeric(0),
  Hs = numeric(0),
  alpha = numeric(0),
  alphas = numeric(0),
  delta = numeric(0),
  period = 0,
  debug = FALSE,
  ident = 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.

dfrac

The fractional differencing parameter.

dfs

The seasonal fractional differencing parameter.

H

The Hurst parameter for fractional Gaussian noise (FGN). Should not be mixed with dfrac or alpha: see "Details".

Hs

The Hurst parameter for seasonal fractional Gaussian noise (FGN). Should not be mixed with dfs or alphas: see "Details".

alpha

The decay parameter for power-law autocovariance (PLA) noise. Should not be mixed with dfrac or H: see "Details".

alphas

The decay parameter for seasonal power-law autocovariance (PLA) noise. Should not be mixed with dfs or Hs: see "Details".

delta

The delta parameters for transfer functions.

period

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

debug

When TRUE and model is not stationary/invertible or identifiable, prints some helpful output.

ident

Whether to test for identifiability.

Details

This function tests for identifiability via the information matrix of the ARFIMA process. Whether the process is stationary or invertible amounts to checking whether all the variables fall in correct ranges.

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

If dfrac/H/alpha are mixed and/or dfs/Hs/alphas are mixed, an error will not be thrown, even though only one of these can drive the process at either level. Note also that the FGN or PLA have no impact on the identifiability of the model, as information matrices containing these parameters currently do not have known closed form. These two parameters must be within their correct ranges (0<H<1 for FGN and 0 < alpha < 3 for PLA.)

Value

TRUE if the model is stationary, invertible and identifiable. FALSE otherwise.

Author(s)

Justin Veenstra

References

McLeod, A.I. (1999) Necessary and sufficient condition for nonsingular Fisher information matrix in ARMA and fractional ARMA models The American Statistician 53, 71-72.

Veenstra, J. and McLeod, A. I. (2012, Submitted) Improved Algorithms for Fitting Long Memory Models: With R Package

See Also

iARFIMA

Examples

IdentInvertQ(phi = 0.3, theta = 0.3)
IdentInvertQ(phi = 1.2)