lARFIMAwTF {arfima}

Exact log-likelihood of a long memory model with a transfer function model and series included Computes the exact log-likelihood of a long memory model with respect to a given time series as well as a transfer fucntion model and series. This function is not meant to be used directly.

Description

Once again, this function should not be used externally.

Usage

lARFIMAwTF(
  z,
  phi = numeric(0),
  theta = numeric(0),
  dfrac = numeric(0),
  phiseas = numeric(0),
  thetaseas = numeric(0),
  dfs = numeric(0),
  H = numeric(0),
  Hs = numeric(0),
  alpha = numeric(0),
  alphas = numeric(0),
  xr = numeric(0),
  r = numeric(0),
  s = numeric(0),
  b = numeric(0),
  delta = numeric(0),
  omega = numeric(0),
  period = 0,
  useC = 3,
  meanval = 0
)

Arguments

z

A vector or (univariate) time series object, assumed to be (weakly) stationary.

phi

The autoregressive parameters in vector form.

theta

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

dfrac

The fractional differencing parameter.

phiseas

The seasonal autoregressive parameters in vector form.

thetaseas

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

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".

xr

The regressors in vector form

r

The order of the delta(s)

s

The order of the omegas(s)

b

The backshifting to be done

delta

Transfer function parameters as in Box, Jenkins, and Reinsel. Corresponds to the "autoregressive" part of the dynamic regression.

omega

Transfer function parameters as in Box, Jenkins, and Reinsel. Corresponds to the "moving average" part of the dynamic regression: note that omega_0 is not restricted to 1. See "Details" for issues.

period

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

useC

How much interfaced C code to use: an integer between 0 and 3. The value 3 is strongly recommended. See "Details".

meanval

If the mean is to be estimated dynamically, the mean.

Value

A log-likelihood value

Author(s)

Justin Veenstra

References

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